pcitgis WordPress core has multiple capabilities that determine how user can manage content (posts, pages, media or CPTs). That is the first authorization layer. For example edit_posts, edit_pages, edit_published_posts etc. If your custom role does not have proper capabilities assigned, users will not be able to edit content even if they are authors.
The second layer of content authorization is defined per post type. When each post type is registered, even WordPress core post types like post, page or attachment, during registration, declare capabilities that are assigned for specific actions (for more info check get_post_type_capabilities reference).
The final layer of content authorization comes with AAM as it overrides access controls to a content if it was not already blocked by WordPress core with two other layers.
So you have to pay attention to capabilities that user has as well as access settings that are defined to a role on Posts & Terms tab.
If necessary, I can help to prepare the Access Policy that will define all the necessary access controls, just keep me posted.