Qubes_dom0-root does not exist - preventing boot after ungraceful shutdown

Can you post the errors that you have in rdsosreport.txt?
Maybe only root thin pool was corrupted and you can try to recover it.

If you’re able to decrypt the LUKS and your LVM is not corrupted then you can try to get the data from the qube like this:

But you won’t be able to backup the qubes themself to restore them in new Qubes OS late, you can only get the data inside the qubes like this. You’ll have to recreate the qubes in the new Qubes OS installation manually.