I don't have "2 buttons" on the screen titled "Permission not granted", and no file dialog. Also not working, when asking VLC to play the file from another program. Must be a bug or incompatibility somewhere. Also this must be the reason why I wasn't able to find a music player on F-Droid then :| Thank you for checking!
Steps:
0. Uninstall VLC (I just did this to reset its permissions+config)
1. Install VLC (3.5.4 from fdroid)
2. Open VLC
3. It'll start with a splash screen, click next.
4. Next screen is VLC asking what permissions you want to give it. Pick the leftmost of the 3
5. Finish the setup wizard
6. It prompts for notification permission, which I allowed
7. You should be at a screen titled "Permission not granted", with 2 buttons. Click the right button to pick a file
8. Use the system file dialog to pick a file
9. It plays