He's currently 78, and would be 86 at the end of his 2nd term, the oldest president in history by far (He would be just under a decade older than the runner-up, Ronald Reagan, at 77).
Personally: I don't think so.
My best detailed guess: Sometime before 2024, he'll step down and hand the torch to Kamala due to "health reasons" (I think we all agree that something's up with that dude's brain, and it'll probably reach a point where they can't even pretend to hide it anymore) and, depending on who her opponent is, she could very well lose.
He could also just. like, die at any second since he has glass bones and paper skin, which would be hilarious. Tho he does unfortunately have access to literally the best healthcare in the world, which was enough to save Trump from covid, so take that as you will.
My theory is that like you say, he'll pass the torch to Kamala before the end of the first term, setting her up as the presidential candidate in 2024.
Or he trips over another dog and dies.
I'd say it's a toss up between him intentionally stepping down vs. pulling an RBG and sticking out his first term when he clearly should just give it up. I don't think he'll run again, and him not stepping down would also fit with general Democratic incompetence (running a VP in a primary is likely a weaker position than running Harris as a sitting president).
The next decade is going to be a reboot of Veep only worse :sadness: