But is there any obligation on the part of the club other than his wage?
If Koeman orders him to train individually and never calls him up for any games, does he have any legal ground to challenge that?
Yes for making him train individually, no for not using him in games.
All players under contracts have right to train with the team unless there are some serious disciplinary issues like missing out on trainings, doping etc. (these things are all mentioned in players individual contracts and also in club's internal codecs that all players are aware off) but Barca needs to have evidence for that if a player would file a complaint with AFE (Association of Spanish Footballers). What we can't do is discipline a player for being on high wages (not his fault) or not wanting to leave (Umtiti)/ not wanting to renew (Ilaix) by not allowing him to train with the team.
So the only thing club can do is not play him. This is club's/coaches decision. Nobody from the outside could prove that he's not playing as a punishment rather than him just not being good enough or not fit into Koeman's plans as good as other players at his position.
But if he cares more about money than actually still getting something out of his career (which is probably true at this point) then Umtiti will just happily accept being on the sidelines collecting his pay checks for next year or two.