As long as you're willing then let's overthink this some more...

According to the hand-written note I found from the gunsmith I got my parts from, the slide stop is the same for the 645, 745, 4506 (no dash), 4516 (no dash), and 4516-1. I have no way whatsoever of verifying this.

From an engineering standpoint (I started out many moons ago in marine engineering), the pivot post on the slide stop had a dimple in it where the end of the recoil spring guide rod rests. If this dimple is just slightly off, worn on one side, or the tip of the spring plunger in the guide rod is worn unevenly - and yours appears quite worn but I don't know the specs - then it could displace the slide stop laterally just a fraction, which would push the tab that catches the slide outward until the fault you originally describe occurs.

Also, if the bent end of the side plate assembly is angled outward slightly, then that would push the spring loaded plunger on the end of the slide catch outward as well (as shown in your second batch of photos) aggravating the same issue.

Of much less likelihood (MUCH less...), the whole slide stop could be deformed outward from excessive use, also aggravating this issue.

Impressed yet?

Regardless, the solution all seems to be the same - replace the slide stop and the side plate assembly. Possibly even the recoil spring guide rod plunger tip as well.

And after all that, I need a nap!