Distrobox containers breaking probably will happen eventually regardless. They are intended to be remade as the nature of them. You may want to look into distrobox-assemble since you can make your own declarative boxes that include all the packages you want. I’m not actually sure what happens if you stop the update mid-way since they are based on non-atomic Linux distros, so they could break if the upgrade is halted midway through from I’d assume but someone can correct me if they know for certain.
I wanted to point this out though that Flatpak updates can be stopped midway and shouldn’t break, but if you do have issues with Flatpaks, use Warehouse (preinstalled) to downgrade applications, delete userdata, etc.