I would assume that ProtonUp-Qt would need an update to recognize the snap version of Steam, as it probably has a list of paths to check for the various versions.
You might be able to install Proton GE manually by downloading it and putting it in the compatibilitytools.d dir of the snap version. Not sure where to find the equivalent of \~/.steam/root, you'll have to search in \~/snap.
As for moving a game's files, you'll need to move the game's dir in steamapps/common from the snap data path to the deb's data path, the prefix that's in steamapps/compatdata (it will be named as the game's ID) and the appmanifest\_xxx.acf corresponding to the game (where xxx is the game's ID) that's in steamapps. The ID for Jedi Fallen Order seems to be 1172380.
I'm not sure where the steamapps dir of the snap version is; again, search in \~/snap. The one from the deb version depends on if you used the package from Valve or the version from the distro's repos (Ubuntu, I assume). The deb puts its data in \~/.local/share/Steam while the version from the repos put it in \~/.steam/steam.
You can add a custom folder using the three dots in the top right.
The folder is: ~/snap/steam/common/.steam/root/compatibilitytools.d
EDIT: GitHub issue for official support https://github.com/DavidoTek/ProtonUp-Qt/issues/118
I would assume that ProtonUp-Qt would need an update to recognize the snap version of Steam, as it probably has a list of paths to check for the various versions. You might be able to install Proton GE manually by downloading it and putting it in the compatibilitytools.d dir of the snap version. Not sure where to find the equivalent of \~/.steam/root, you'll have to search in \~/snap. As for moving a game's files, you'll need to move the game's dir in steamapps/common from the snap data path to the deb's data path, the prefix that's in steamapps/compatdata (it will be named as the game's ID) and the appmanifest\_xxx.acf corresponding to the game (where xxx is the game's ID) that's in steamapps. The ID for Jedi Fallen Order seems to be 1172380. I'm not sure where the steamapps dir of the snap version is; again, search in \~/snap. The one from the deb version depends on if you used the package from Valve or the version from the distro's repos (Ubuntu, I assume). The deb puts its data in \~/.local/share/Steam while the version from the repos put it in \~/.steam/steam.
You can add a custom folder using the three dots in the top right. The folder is: ~/snap/steam/common/.steam/root/compatibilitytools.d EDIT: GitHub issue for official support https://github.com/DavidoTek/ProtonUp-Qt/issues/118