com VS net.sourceforge.tomatoes.IHaveNoTomatoes

Flatpak apps can still have access to the host ressources, like the file system. The nice thing is that you can see those permissions beforehand and adjust them if necessary. Flatseal simply has the permission to make those adjustments for other flatpak apps. Take a look at Flatseals manifest file, that should make it obvious.

Protontricks

Look at https://github.com/flathub/com.github.git_cola.git-cola/ which has git as a runtime dependency.

Click the link that says "See details" which leads to this page

Hi all, I've installed the flatpak version of ungoogled chromium on my ubuntu 20.04 machine and it has been working like a charm. However, I need to apply a policy .json file. In deb chromium I would put it in /etc/opt/chromium/policies/managed/. On flatpak version I am not clear on what folder to choose. I obviously tried using /etc/opt/chromium/, /etc/opt/chrome, /etc/chromium, ~/.var/app/com.github.Eloston.UngoogledChromium/, ~/.var/app/com.github.Eloston.UngoogledChromium/config/chromium/ but all without any results - the chrome://policy page in chromium is empty and doesn't show any policy to be set. I found that the flatpak "extensions" are used, but I didn't find any documentation on how to use this. I also tried giving the app access to the whole disk using flatseal but no avail.

Flathub (Linux)

I am not familiar with the process at Flathub. But as far as I understand, the developer of CopyQ has already made an appropriate update (https://github.com/flathub/com.github.hluk.copyq/pull/53). Maybe these updates will be shown at flathub.org only with a time delay.

Now, what I was trying before just setting the version was to use protontricks, you can install it in the software repository in desktop mode. Then follow the flatpack install instructions

There's a script for that here: https://github.com/flathub/com.github.Eloston.UngoogledChromium

GNOME runtime bump to 43 for Haguichi is now merged. Might take a few hours to get published.

...and, for the record, I'm the maintainer of the net.sourceforge.tomatoes.IHaveNoTomatoes Flatpak and I did the legwork to get the io.sourceforge.pysolfc.PySolFC Flatpak published before handing it off to PySolFC upstream to maintain (among other things, those PySolFC screenshots were taken on the computer I'm typing on right now), so I think I know a non-zero amount about how this stuff works.

Your Appstream XML and .desktop file are unsatisfyingly sparse. (Compare the ones from the aforementioned I Have No Tomatoes flatpak that I maintain.)