All I could find is how to make a list, and reinstall flatpaks from that list, as well as backup app data, however all of that assumes I want to do updates.
Meanwhile what I want is akin to extracting APK of a stable version of some app, backing it up and using it for years to come. For example that's how I joined these 2 screenshots, using JointPics from 2014 which isn't even on Play Store anymore, and targets API so low that it has to be installed via ADB. (Yeah, I am too dumb for GIMP)
As for the regression, you can see. On left is older Flatpak, on right is version from Arch repo. The Flatpak I originally installed as a hotfix for update that broke it completely at one point on Arch.
You can see the older version nicely fits the screen, splitting up text into columns.
Meanwhile the new version just does smaller page in middle of screen that doesn't even work properly with Breeze Dark theme, causing different background for text sections.
The only improvement is ability to flip pages rather than use arrows, but that's minimum.
Well, and maybe the progress keeping got fixed, but I didn't test that much.
Don't pay attention to the taskbar. I wish it could flip to vertical with different screen orientation. Yeah, the icons' clickability is a dice roll of what you tap.
You can use the Warehouse app to do this: https://flathub.org/apps/io.github.flattool.Warehouse
Wouldn't recommend doing it with the CLI, they don't make it easy.