Hey, thank you for testing it out yourself. I feel like I'm losing my mind here as if I'm missing something super obvious.

The only options when inspecting Alexander are to look at 1) his face, 2) his hands, and 3) his robes, each of which just presents a narrated line with no option to get the gem. Even loading the game from the final fight area on Fort Joy gives me the same issue, so whatever it is, it's already occurred before I leave Act 1. Perhaps I'll try to re-install if by some very unlikely chance that helps.
There is another (I'm assuming) unrelated bug here, where if you talk to the Magister from outside the locked cage door, sometimes the door magically unlocks and opens automatically. I have no idea if the state of the door has anything to do with the spawning of the Strange Gem. Also, the cage guard mentions she dropped the key somewhere, and I've never found it on any of my playthroughs (I assume it's to encourage you to get in via teleporting or lockpicking), if it exists at all.
If I'm still up the creek after the re-install, I'll try to get some video footage of it to submit to Larian. The only game mod I play with is the Sprint mod, and as far as I can tell there isn't any documentation of that causing any sort of issue like this one.