Did S&W just send you those springs? Or did you just order them from some other vendor online? (If you don't mind me asking, that is.)
Anyway ...
The #10087 spring is the standard spring for the 5906TSW. It's an unpainted, "plain color" steel spring. It used to be listed as a revised (R-1) spring for the earlier 5906 series. (It was also the R-4 spring in the older 4006, and is now also the standard spring in the 4006TSW, as well.) It's what I'd try first as a repair spring.
The #23864 spring is painted white (sort of washed out, but white). It's a Lighter-than-Standard spring for the 59XX series guns, meaning lighter than the #10087 spring.
Part of replacing an extractor spring involves checking the tension using the appropriate hook attachment on a Wagner force dial gauge (the tool's hook is used to exert outward tension on the extractor hook until movement - deflection - is detected at the tail, which is when the tension reading is checked).
The normal recommended tension range for extractor springs changes depending on the style (vintage) of the 9mm slide. The style is determined by the width of the barrel tab cut, which means whether it's the older narrow barrel tab model or the newer wide barrel tab model. The old narrow barrel tab slide will also have the machined rounded "shoulders" present above where the case base sits when centered in front of the firing pin hole, while the wide barrel slide will have a "straight" cut up & down the breech face, lacking the older machined shoulders to support the "top" of the case base.
The narrow barrel tab 9mm slides run 4-8 lbs for the extractor spring, and the wide tab slides run 7-11 lbs. There can be exceptions, but if the normal spring weight is not met after replacement, the gun ought to be returned to the company for some fine tuning in getting the spring tension to work right for that particular gun. (There was a previous "repair set" of springs for the early 3rd gen 59XX guns that was a nested set of springs, and the tension could sometimes vary a bit above normal as long as normal feeding was not compromised, but that nested set is now "obsolete".)
Now, the older the 3rd gen 59XX gun, the more likely there might be some variation in the dimensions of the extractor spring hole in the slide. That's because of the older machining methods used. The hole might have an incomplete cut at the bottom, with a rounded edge around the bottom of the hole, not allowing the spring base to sit flat, and making the spring seem too "long", and therefore too strong. Hence the occasional need for a lighter spring that could be compressed more easily (or a technician might use the appropriate hand turned end mill to reshape the bottom edge of the hole to accept the right spring, but that obviously isn't a "kitchen table fix" since it takes some skill and experience).
Even if the spring tension "reads right" with the force dial gauge, though, the real test is whether the spring works right in that gun, using live ammunition (of the type normally expected to be used in that gun).
If the spring is too heavy, there may be feeding problems. If it's too light, there may be failures-to-extract. That's why the bench checks are just part of the diagnosis and repair, with live-fire being needed after successful bench checks to confirm the new spring meets recommended spec for tension, AND actually gets the gun to run as intended.
The newer production guns are much tighter when it comes to tolerances, but if you look at the parts lists you'll see that even then there's usually 3 extractor springs listed for the TSW's. Older models can have 1-2 springs listed. The first one is usually the standard production spring, with the other ones being optional springs that might be used by a technician or armorer when getting any particular gun to run within spec (could be lighter or heavier than standard, depending on the caliber/model).
Replacing an extractor spring in an older S&W can be almost as much art as science.
Also, the extractor pin must be removed out the bottom of the slide, and reinstalled from the bottom. They're often very hard to get started moving, with a "starter" punch usually needed before the standard cup end pin punch is used to complete removal. They should be flush with the bottom of the pin hole, and any burrs left behind carefully dressed so they don't contact the frame rails which run below the extractor pin. S&W used to provide a narrow offset revolver file for this task, as well as a tapered needle reamer to use (from the bottom) in case the pin hole needed to be dressed (but which could also damage a slide's pin hole if used improperly and unnecessarily).
This sort of repair is best left to those folks who have some knowledge, experience and the right tools. Once you damage a slide, there aren't any "oversize" extractor pins available. I've had the slide of an issued 9mm ruined when someone apparently tried to remove the extractor pin (improperly and without authorization), buggering out the bottom of the hole with the wrong tools to the point where it would never hold a pin tightly again. The slide is an expensive part of the gun to replace, second only to a frame.
Think about either returning the gun to S&W for repair, or finding a local gunsmith familiar with 3rd gen guns who has the right tools for the task.
Just my thoughts.
