INFO paperwork.frontend.settingswindow Got value [['Brother ADS-2100e', 'sane:net:127.0.0.1:brother4:bus3;dev2']]
(...)
ERROR paperwork.paperwork ../subprojects/libinsane/src/workarounds/cache.c:L568(cache_get_device): Failed to get_device(sane:net:127.0.0.1:brother4:bus3;dev2): 0x40000003, Invalid value
Hm, so this is not simply the device ID changing.
My guess is that the problem is due to the use of the Sane Brother backend and the Sane backend net together (you have to use the Sane backend net since Flatpak runs applications in containers). Since the Brother backend is proprietary, I think this is close to impossible to debug.
What you can try is to install Paperwork without Flatpak (and therefore not usethe Sane backend net). By the way, Paperwork 1.3.1 is available in Debian testing: https://packages.debian.org/bullseye/paperwork-gtk .