So what happens if Biden dies in office, say, in the next six months. Are the Dems necessarily doomed to lose in 2024? Is no "rally around Kamala" possible?

If Biden dies in office prior to the convention (or after the convention, for that matter), they're in a world of trouble.

No, a "rally around Kamala" isn't really possible. I mean, it's theoretically possible - it doesn't violate the laws of physics or anything - but it just won't happen. Sure, as the Veep she's got a strong position to try to grab the nomination. But she's just not popular enough to be the nominee by acclamation - and it's too important a political asset for everyone to step back and let her (or any other person) take it in order to avoid a fight. Someone will fight her for it. Probably a lot of someones.

If Biden actually died, they could probably get consensus to change the convention rules to release the delegates. It would probably be pretty chaotic, and it might be brutal.

But even if it weren't....you end up with a nominee that's then has to build a national campaign from scratch in only three and a half months. They walk out of Chicago with no national staff, no fundraising in place, no ad buys locked up, no campaign calendar, no groundwork.....just starting from jump.

Yep....doomed to lose.