Running from command line is not an option since this is a flatpak installation

And there might be the cause of your problem. Don't use a flatpak installation. The creators of flatpaks seem to think they know better what to pack and most likely have stripped the java runtime. That it works at all on your desktop is plain luck.
Download the 7.5 .tgz and extract it in a directory of your choice. Start Sweet Home 3D with the SweetHome3D_Java3D-1_5_2 script.
The .tgz comes with the correct Java runtime included and using that avoids all kinds of problems. It doesn't interfere with an existing
Java install.