First and foremost, I feel terrible for Dame. To go from dealing with some scary real life medical stuff, to probably rushing back too soon in an effort to help his team in what was a longshot to begin with, to now blowing out the Achilles and looking at missing all of next year before coming back in likely diminished form at age 36.
As for Giannis, my gut feeling is that he cares more about being a One Team Guy like Kobe or Duncan or Dirk than he does about maximizing his Ring Odds, so he won't ask to be traded this offseason. I think he would view demanding a trade (especially now after Dame's injury) as taking the easy way out, which would seem to go against his character.