Did you come to try signing the app package?
I do have the permission issues on an M1-Mac, as well. With me, (Spine-)Godot is requesting access to a removable volume which makes sense because my projects folder is located on an external SSD. However, no other application on my system (including normal C#-enabled Godot) has that issue. In fact, I am experiencing it the first time ever, now that I'm trying to use Spine with Godot.
Enabling access in system settings doesn't help nor does granting Spine-Godot full disk access. Running the terminal command that zjjt mentioned results in the message "---deep: no identity found" for me with no further effect.
Googling the issue, people seem to have solved it with other software by notarizing the app with Apple, which appears to be nothing complicated but requires App Developer status which costs 99$/year.
Perhaps that's something you guys could do?
It's not a software-breaking issue, of course, but it's a hell of a lot annoying to have to click "Allow" two to six times on every opening of Godot and every little build you try to playtest.
For me, it voids the speed advantage Godot used to have over Unity. Compilation is super fast, but then I have to click "Allow", "Allow", "Allow", "Allow" before the build plays, sigh ..
Edit: Okay, at least for builds, I too can avoid the issue by moving my project folder to my primary disc. That's inconvenient, because I have the M1 mac mini with the smallest internal drive (128 gigs, almost full) and now need to keep my spine-enabled Godot projects separate from all the others. But it's better than the alternative, for the time being.