How do I add a new group permission?
I found the answer to this question here: https://www.drupal.org/project/group/issues/2959912

Create a .yml file, for example: my_module.group.permissions.yml

It should contain:

access group menu edit:
  title: 'Edit group menu'
  description: 'Allow users to edit the group menu'


First line is the permission itself.  I did this. Flushed cache, and my permissions now appear in Group module permissions screen under "My Module".