I think Bush, whatever people think of him when he was in Office, is acting Presidential. His dad went further though. The closest Dubya has gotten, on record, is oblique references to press freedom.
We don't really know what he said during the 2017 inauguration; its apocryphal, it kind of fits with his public character, but its better that he just stays silent on the matter. Irrespective of my opinion of a current President, past holders of the office should maintain a statesman like dignity, partly because they know the reality of that office, about what really goes on behind closed doors, and the difficult decisions all Presidents have to take, and life with. And it cuts both ways with a current leader commenting on his predecessor. In both cases, the Head of State represents ALL Americans, not just the ones who voted for him. I'd say the same about Prime Ministers, but constitutionally, that Office is entirely different, and the PM is merely First among Equals (PMs are easily replaced).
https://www.politico.eu/article/former-presidents-walk-fine-line-in-trumps-america/#:~:text=Former presidents walk fine line in Trump's America – POLITICO.
Yeah, I don't recall any of the former Presidents embarking on some sort of project in collaboration with the current incumbant; whether that's because they don't want anything to do with him, or vice versa, is not clear.
When Trump shakes the hand warmly of a departing Biden, or is seen sharing a joke with Obama at a funeral, is it genuine, or just for the cameras. Is the very personal criticism of predecessors genuine, or just for effect? He spent 13 years literally acting a role for the cameras.