There's no way Biden will do it out of a sense of morality. It's all about political calculations.
Is the appeal of justice and restoration of faith in the rule of law greater than the risk of turning him into a martyr? You better believe if Trump & his cronies go to trial, conspiracy theories and the right wing media will explode. Even if it can be 100% proven that he committed several crimes while in office (which he did), the backlash may not be worth it, potentially costing them the Senate in only 2 years.
I would think the smart thing to do would be to let the SDNY or Biden's pick for AG handle it. Hopefully it's an unknown career prosecutor and not a big name like Schiff or Harris. We want this to appear as non-partisan as possible. Investigating things like embezzlement, profiteering, and fraud would also be good, forcing his cronies to surrender ill-gotten gains. Time in prison would be much harder federally. I think that would only be possible at the state level.
This is where I'm at. On the one hand, Trump's whole strategy his entire life has been about avoiding accountability by making it too costly to take him down without some severe losses for the other side. We saw it with his bankrupcies, where banks decided he was too big to fail and crushing him would result in severe financial losses for themselves. We saw it with his nomination, where GOP party leadership knew he was unfit for office, but decided he was too big to fail and depriving him of the nomination would result in the fracturing of a party that was already barely hanging on to national competitiveness through a combination of a geographical advantage in the Electoral College, a propaganda network to herd the base and vote suppression and gerrymandering in the states they controlled. We saw it during this term, where even Republican politicians (most of whom really, really do know that Trump is corrupt, incompetent and a rotten human being) stick with him because standing up to him gets you singled out and then kicked out. We may see it if he loses his diplomatic immunity.
We already saw during the impeachment process that Trump was guilty of stuff that would have ended the career of previous politicians, he 100% admitted he did what he was accused of and credible witnesses testified it. And yet, Trump's strategy of flooding the zone with shit eventually caused the vast majority of the Republican politicians (including those who previously said that this stuff was grounds for removal) to move the goalposts and say "yeah, this stuff is fine". The same would happen during a criminal prosecution. His cult will quickly pivot to "yes, embezzlement and laundering is fine". Trump actually landing in jail would almost certainly cause enough of a political backlash to lose Democrats the senate and possibly the house in 2022. The question would be whether poetic justice on a man who spent his entire term gleefully flaunting breaking the law would be worth turning a presidency that could potentially get stuff done back into a lame duck and shut down the restoration of the judicial branch. The State of New York going all in on him would probably provide SOME political cover, though it'd be still be blown up into a political retaliation scandal by the right-wing media. Once he'd be in jail and deprived of his platform, additional federal charges silently trinkling in afterwards and adding to his sentence would make much less of a splash.
not going after him will probably be Biden's "olive branch" to the remaining Republicans in Congress to get things back to "normal". It won't work, but he will try.
The ironic thing is that having Trump thrown in jail would be the greatest gift he could give them. A large amount of Republican politicians don't like Trump. They know how unfit for office he is and they hate having to publically kiss the ass of a man who's so much dumber than they are. They also know that once he no longer has the power to confirm their judges or sign their legislation, they'll still be stuck with him. They'll lose all the benefits while still being forced to deal with all the hassles. Bush was a party creature, so once his popularity dropped and he knew his presence would hinder the party, he had the good sense to silently retreat from the political scene. Trump doesn't care about the party's political goals, he just sees it as a vehicle for his need for constant adulation. So he'll stick around, try to make everything about him and will hang on to his base inside the party with all his might and threaten to go scorched earth if the Romney faction makes attempts to push him out. (which, if Biden manages to flip the senate, will almost certainly be attempted) Heck, he'd either insist on running again in 2024 or try to turn the 2024 primaries into a season of The Apprentice, with candidates having to kiss his ass on television. You think the party leadership WANTS that?
There's been a lot of fear of the GOP nominating a "smarter Trump" next time, but ironically that'll remain a lot more difficult as long as the original sticks around because in Trump's mind there's no such thing as a smarter Trump who isn't him. He'll refuse to stay out of the newcomer's way because he can't bear to play second fiddle to anyone. He'll be what center-leftists feared Bernie Sanders would be before the latter proved them wrong by fully getting behind Joe Biden.
So the question remains what would be most politically beneficial. Throwing Trump in jail and giving Republicans who secretly hate him the ability to gleefully fundraise off his misery? Or letting Trump be part of an intra-party civil war because the man can't see when his presence is no longer beneficial?