There is a well-documented issue where Flatpak Bitwig can’t access plugins in /usr/lib/vst3, /usr/lib/clap, etc. I have not seen anywhere online where anyone has figured out how to make this work, even with the use of Flatseal.
However, you can get around this by running the “bitwig-studio” executable in /var/lib/flatpak/app/com.bitwig.BitwigStudio/current/active/files/. Running it this way will pick up the plugins!
I suspect that running it this way basically bypasses the Flatpak container. But hey, it works!