SUMMARY
This problem does not seem specific to KDE, but could be related to flatpak interaction with Kinoite or Silverblue. 

On Oct 19 I rebased from Silverblue 34 to Kinoite 35; I am using KDE on X11. The same problems happen on gnome on Wayland.  Flatpak seems to be broken, it complains about read only file system. It happens with flatpak update, as well as with update of an individual package, but not with some packages such as gnome calendar.

Additionally it sets the home directory to read only as well, causing all manner of problems including being unable to enter any Toolbox, although these other problems can be fixed by rebooting.

I have completed a rpm-ostree update successfully, now I have flatpak 1.12.1 , but the problems remain.

Discover doesn't seem to work all, presumably it uses flatpak.

STEPS TO REPRODUCE
1. $ flatpak update org.kde.kpat # or general update


OBSERVED RESULT

                                                             Branch              Op             Remote              Download
 1. [✗] org.freedesktop.Platform.GL.default                              20.08               u              flathub             < 106.4 MB
 2. [✗] org.freedesktop.Platform.VAAPI.Intel                             20.08               u              flathub              < 11.6 MB
 3. [✗] org.kde.WaylandDecoration.QGnomePlatform-decoration              5.15                u              flathub              < 10.2 MB
 4. [✗] org.kde.Platform                                                 5.15                u              flathub             < 370.4 MB
 5. [✗] org.kde.kpat                                                     stable              u              flathub              < 15.2 MB

Warning: Failed to get revokefs-fuse socket from system-helper: Failed to create new cache-dir at /var/lib/flatpak/repo/tmp: Read-only file system
Warning: mkdirat: Read-only file system
Warning: Failed to get revokefs-fuse socket from system-helper: Failed to create new cache-dir at /var/lib/flatpak/repo/tmp: Read-only file system
Warning: mkdirat: Read-only file system
Warning: Failed to get revokefs-fuse socket from system-helper: Failed to create new cache-dir at /var/lib/flatpak/repo/tmp: Read-only file system
Warning: mkdirat: Read-only file system
Warning: Failed to get revokefs-fuse socket from system-helper: Failed to create new cache-dir at /var/lib/flatpak/repo/tmp: Read-only file system
Warning: mkdirat: Read-only file system
Warning: Failed to get revokefs-fuse socket from system-helper: Failed to create new cache-dir at /var/lib/flatpak/repo/tmp: Read-only file system
Error: mkdirat: Read-only file system
Updates complete.
error: There were one or more errors

$ pwd
/var/home/Me

$ touch test
touch: cannot touch 'test': Read-only file system

EXPECTED RESULT
flatpak update org.gnome.Calendar
Looking for updates…


        ID                          Branch         Op         Remote         Download
 1. [✓] org.gnome.Calendar          stable         u          fedora         22.3 MB / 22.3 MB

Updates complete.



SOFTWARE/OS VERSIONS

Linux/KDE Plasma: 
(available in About System)
KDE Plasma Version: 5.22.5
KDE Frameworks Version: 5.85.0
Qt Version: 5.15.2

ADDITIONAL INFORMATION

Kinoite 35
Kernel Version: 5.14.10-300.fc35x86_64(64bit)
Graphics Platform: X11