A couple quick observations from the video, just regarding potential educational/hobbyist interests.
Use better pin punches.

It's a 1/16" pin punch to depress the ambi lever plunger. A suitably narrower punch than shown can also be used to depress the firing pin and let the manual safety body be pushed
further past the rear of the firing pin in one movement when removing the assembly. Using the right size punch the first time means not having to stop and switch to different (bent??) punch to complete the task. Probably why a bent punch isn't included in the armorer kit.
It's not necessary to rely on tweezers for removing both the ambi lever plunger and its spring. Sometimes the spring remains in the hole, even if you remove the plunger ("button"). You can tip the slide over and gently tap it on your bench or block to let both parts drop out of the hole. (Set them aside with the ambi lever so they aren't mixed up with the body plunger and its spring.)
Use a finger tip to reach over and capture the top of the body plunger (the second "button") as the safety assembly is pushed out of the slide, or you risk having the plunger flying out. It varies from slide to slide, but it's easier to trap and hold the plunger as it clears the outside edge of the slide in the first place. (Eye protection is always a good idea for errant plungers or springs, BTW.)
In the event of badly gunked firing pin, it may be necessary to pull on the rear of the pin to get it free (continuing to depress the steel FP safety plunger, of course) ... and then the badly gunked spring may remain stuck in the channel. Trying to tug on the spring in the wrong manner can risk damaging the spring. (Forgetting to keep the safety plunger depressed isn't helpful, either.) I use a small hooked end of a paperclip to
carefully pull on the rear of the spring, while keeping the safety plunger depressed. Sometimes it's even easier to use the right size Q-tip, slipping it inside the spring and turning it, and letting it 'capture' the spring from the inside, coming out with the Q-tip as you turn and pull it (while keeping the safety plunger depressed).
Armorers are taught to only remove an extractor and/or rear sight base in the event of a problem that requires their replacement (or the replacement of the nylon and steel plungers & their springs under the rear sight). Not for for routine inspections and "cleaning".
Removal of the extractor pin is taught to be done
opposite of how the video states. The pin is driven out the bottom of the slide, from the top. In other words, it's removed top-to-bottom.
It generally requires the use of what is called a "starter punch" in armorer class, meaning a short, stout (often tapered) punch, like a narrow headed nail set ... and possibly some serious whacking with a hammer, especially in older guns. Some of the older guns have extractor pins that are really, really tight. (Some may be really, really, really, really tight.) It may feel like you're hammering like a blacksmith on a particularly recalcitrant pin.
Once the extractor pin is
just broken free and starts to move, then a straight, long pin punch can be used to complete removal of the pin. Lighter tapping. Holding the extractor firmly pressed inside the slide's extractor recess can help prevent the spring from shoving the extractor outward so far & hard that the pin punch is bent. Of course, bent 1/16" pin punches are often handy to be converted into spare "starter punches", by breaking off the bent/damaged tips at the right length near the tapered shoulder.
Armorers used to be given a long, tapered needle reamer to use to clean up any burrs inside the extractor pin hole. The tapered reamer was intended to be inserted from the bottom of the pin hole in the slide. Care had to be taken to avoid needlessly enlarging the pin hole. Wallowing it out. Ugh.
I noticed in my last couple of 3rd gen armorer recerts that the needle reamers aren't included in the tool kits anymore. From what I heard expressed, it might've primarily been the result of increasingly much better machining capabilities for the newer guns since the days of the 90's ... and
perhaps it introduces less opportunity for rambunctious and/or less attentive armorers to create problems for themselves by really wallowing out extractor pin holes?
Notice the term"tapered" used to describe the needle reamer? That means the extractor hole was usually slightly tapered, larger on the bottom of the slide and narrower at the top. Especially in early 3rd gen guns. That means driving out the pin in the wrong direction may be akin to trying to drive out the slightly tapered rear sight base in the wrong direction. You might end up with an enlarged hole on the top of the slide (the hole above the extractor recess), and now you can risk developing a walking pin.
In the older guns it sometimes helps to remain aware of the extractor pin 'orientation' (the original top/bottom), as it can make reinstalling the pin easier. I've come across my fair share of older 3rd gens (when I had to replace/fit new extractors) that had extractor pins where one slightly smaller (less peened?) end went up into the bottom of the hole more easily than the other. Why not keep the same orientation if it makes the job easier?
The pin is installed from the bottom. The extractor has to be held sufficiently compressed within it s recess in order for the pin to be lightly tapped (plastic mallet) up through the bottom hole, the extractor body and into enough of the top hole to hold the pin, and then a flat-ended steel punch is used to complete seating the pin. A suitably sized flat pin punch (look at the size of the groove machined to clear access to the pin's hole on the bottom of the slide).
In newer production guns the bottom of the slide has a lightly relieved circular area surrounding the base of the extractor pin. Helps to keep any sharp edges of the pin's bottom from reaching the top of the frame. (FWIW, I use a flat-end Starret punch the size of this relieved area to complete seating of extractor pins.)
Anyway, in the older classes they also used to provide an offset revolver double-headed file, which was used to clean up and remove any burrs from around the bottom edge of the pin and pin hole. The narrow, thin head of the offset file could easily slip inside the frame rail next to the extractor pin base and lightly remove any raised burrs. Obviously introducing an aggressive cutting file into the frame rail could be an easy way to really change metal surfaces from how they ought to be, and care was emphasized. (Another tool 'missing' from current 3rd gen tools kits.

)
The "plate" holding down the plungers and springs underneath the rear sight base was introduced on the wide (.45/10) slides. The older production 3rd gen 9/.40 slides didn't have the oval machined to accept the plate, but just the separate holes for the plungers and springs.
It's surprisingly easy to damage a spring - (bent, tweaked, kinked or even a cut piece off the end of the coil) - when reinstalling the rear sight on a slide which doesn't use a spring plate. It's easy to have happen when the left edge of the sight base is being advanced over the each spring, and the spring isn't being kept 'centered' (light pressure and adjustment with a thin pin punch tip) as the sight base is advanced over each hole/spring.
While I prefer to use an appropriate sight pusher nowadays, armorers are taught to use a brass drift to remove a sight base. I may sometimes use a plastic mallet to lightly start a rear sight into the dovetail so it's held in place too be picked up by the sight pusher (for reinstallation), but I was never taught to use a hammer to directly whack the sight base itself. (Even a brass drift can leave residue "marks" on the side of a sight base, but often the brass residue can be cleaned off.)
I'd not want to be hammering directly onto the rear sight base ... and especially not if it had glass night sight tubes in it.
The front sight base requires the right size brass tipped drift punch judiciously positioned against the side of the
base. The presses which seat the sight bases are powerful. It might require some surprising application of a 4oz ballpeen hammer to break them loose and remove them. Hitting the small front sight post, instead of the front sight's base, is a good way to snap off a front sight (either during removal or installation). Also, night sight tubes can be sensitive to the shock of impact, too, right?
Some guns might have dimensions that are on the generous end of spec, making it easy to drift and remove a sight base. We had a new 4006TSW that had a drifting rear sight base ... to the LEFT. To the tighter end of the dovetail cut. Weird, right? Since I had other things to occupy my time, I had the gun sent back to the factory so they could see if they thought it was the sight base or the dovetail which was out-of-spec. We got it back with a new rear sight ... which once again drifted LEFT under continued recoil.
The gun went back again, with a phone call to a contact in pistol repair, and the gun was more closely examined. It came back with a new slide, as it was finally decided that the dovetail cut was out-of-spec. Ran fine until eventually taken out-of-service when changing to new guns.
I was told in my last armorer recert that the factory had finally determined some correct sizes for coil (spring or roll) pins to be substitutes for the solid extractor pins. Hallelujah. I'm guessing it was because they'd finally switched from solid to roll pins for the M&P 9/.40 slides (the .45's had them from the get-go, which is another story). Anyway, I was told they weren't listed in any parts list, and I'd have to call back and specifically ask for the correct roll pin size for the particular caliber 3rd gen I was repairing to be looked up in-house ... except then I was told the new computer parts system doesn't even include 3rd gen parts (remains in previous system), and not everyone might know how to find the right roll pin for me. The last set of some assorted spare extractor pins I received were all solid, though, so maybe they're still using up whatever remaining solid pins they have in parts. Dunno.
I do know that the guns provided for armorer training always include a regular gun (last one was a new 5906TSW per student), AND an extractor/sight gun. Why? Because frequent removal of the extractor pins and sight bases widens and wallows out the pin holes and the sight dovetails, essentially trashing those slides. The regular student practice guns can be refurbed and sold when they're cycled out of training, without their slides having been damaged in the same manner as on the 'extractor/sight' class guns.
Just some thoughts. I'd be careful (especially if an owner/hobbyist) of doing something just because I saw it in an online video clip. 3rd gen's aren't being made anymore (outside of some few instances of some pre-existing LE agency customers, and those are being pressured to change over to M&P's), and even when they were cataloged and in-production, they didn't grow on trees. The cost of a new slide is a bit prohibitive, even if available.
FWIW, I once saw the end result of a new employee thinking his issued 3rd gen needed a better "cleaning", which apparently meant (in the employee's mind) removing the extractor, and he apparently attempted to drive out the extractor pin upward, using who knows what tools (he was denying involvement and wasn't saying, it seems). The final result was a slide with a really nastily damaged area making up the bottom of the slide's pin hole. There was no way that bottom pin hole was ever again going to hold an extractor pin tightly enough to keep it from moving. The top hole (above the extractor) didn't seem all that tight anymore, either, but the visible damage was all on the bottom of the slide. It sort of looked like someone had been chiseling an excavation around (and on) the base of the pin, trying to drive it upward. That slide was toast, and the gun was pulled from service.