Aren't most of the claims of immunity because congress is supposed to be the one that holds the president accountable? So as long as the House doesn't hold the president to account, they can do anything... but clearly Democrats are more willing to prosecute those in their own party than Republicans... so it's far more likely that Biden would face consequences for his actions than Trump did.
Biden could just resign, if a successful impeachment is a pre requisite of prosecution. Kill Trump, fiften other Republicans spread between the House, Senate and SCOTUS, immediately resign.
That introduces all sorts of timeline issues because you can't impeach someone who isn't in office anymore. It stands to reason that resigning, or ending your term, shouldn't immediately prevent prosecution since often these kinds of cases take years to put together even with a congress that wanted to impeach. Hell, the evidence of illegal actions may not have even come out until after they resigned, in which case congress would never have an opportunity to hold them accountable.
See, you say they can't impeach someone who isn't in office, I'm pretty sure they actually can but usually just don't bother because there didn't used to be much point.