More spoilers are out (more accurately a summary of the chapter by Herms) and yes, Jiren has a bunch more characterization, all of which I think the anime will probably get to by the final fight with him.
According to that…
! Jiren is a good guy going around protecting the weak, but very principled - he refuses to kill anyone, even the villains and will only break his principles for his wish. He's even okay with U11's demise if it happens to go that way and just there in the tournament to get the Super Dragon Balls. So, if we apply that to the anime, that's why he isn't more active. It's a parallel to Goku in a different way and explains why U11 would be supportive of him. He's probably from one of the erased universes and his wish probably is to wish back his universe, which is, I think, the best assumption to make.
I feel like it kind of ruins it for the anime if it's the same because the anime is clearly building up to make his motivations a reveal of sort. It keeps people speculating, even if it leaves him kind of dull for a while.
On the other hand, I can't stand manga Goku. Almost every chapter there is a moment emphasizing how dumb and/or incompetent he is.
! More math test jokes and he's the one to suggest Goten and Trunks, when he would be the one to know their weaknesses. There is the explanation that he didn't witness either Gohan's and Goten's birth, which actually doesn't mean he wasn't there or anything, just that he probably arrived late and still named Gohan, which can make sense.
It's just that it feels very ungraceful and overblown writing. Manga Goku is literally the caricature of his character and genuinely makes me angry.