I don't know by heart if it's able to do your bidding, but perhaps it's worth checking out penguins-eggs. I guess the following would be its elevator pitch:
"penguins-eggs is a console tool, under continuous development, that allows you to remaster your system and redistribute it as live images on usb sticks or via PXE.
The default behavior is total removal of the system's data and users, but it is also possible to remaster the system including the data and accounts of present users, using flag --clone. It is also possible to keep the users and files present under an encrypted LUKS file within the same resulting iso file, flag --cryptedclone.
You can easily install the resulting live system with the calamares installer or the internal TUI krill installer."
Bazzite does allow easy install of EmuDeck and RetroDECK during first installation, which should cover most of your emulation needs. For completeness' sake; Batocera does exist. However, I'm not sure if it runs e.g. Steam games as good as Bazzite runs retro games.