One correct and complete solution:
Use mono’s mkbundle to generate a real executable.
Add full disk access to that.
(This currently has to be redone on updates, but could be made part of the update process).
On a mac, go to /Applications/Sonarr.app/Contents/MacOS
run mkbundle --simple -o Sonarr nzbdrone.exe
It should generate a standalone executable named Sonarr that can be added for full disk access and will work properly.
Of course, you still have to start it separately, but that should be fixable in sonarr itself, since mkbundle works correctly on every platform mono supports.