So it seems as though I there isn't anything I can do on my end without an official developer license or something of the sort. However I did find this page from the Godot documentation that shows ways you can try to run it anyways. If it's any help, I gave it a bundle identifier but had Notarization disabled on export.

Article: https://docs.godotengine.org/en/stable/tutorials/export/running_on_macos.html