After applying patch "xthread_fix.patch" and siebenmann's patch posted here: https://github.com/fvwmorg/fvwm3/issues/818#issuecomment-1401144381
The issue seems to go away, when using fvwm 2.7.0 source code, icons are displayed as it should, after restart, application fullscreen change, etc. But, maybe, there is a reason to wait for a more official solution, as a main FVWM developer is aware about this issue in all FVWM 2/3 versions when using new GNU/Linux distributions.