I think you misunderstand the point of atomic still. Your base system should be installed entirely through ublue or other. Every time you update ublue will hash it and you can go back to that exact config with a working base system. Flatpaks and distrobox are user applications and should store all the data they need somewhere under your /home. Back up your /home and /etc with rsync or similar. When all is said and done your be able to recreate your system with ublue, and restore your configs and personal files with rsync.
The advantages of ublue is you can easily share or restore your base system without needing to backup gigabytes of data every update