A Project Admin clicks on the gear menu of a Custom Page, the only options shown are Copy Page and View Full Screen.
Why isn't this Project Admin allowed to edit page settings and add Apps to the page?
The lack of Admin options on the gear menu indicate that even though the user is a Project Admin, they do not have Admin access to All Projects where the page is shared.
To verify this, a Workspace or Subscription Admin can click the gear menu and select the Edit Page option. From the popup window select the Sharing tab, this will show all projects (or Entire Workspace) where the page is shared. You can select the Show Select Projects Only option to list the projects where the page is shared.
In order to administer the page, the user must be a Project Admin in all of the selected projects. If however, you don't want to give the user Admin permissions to additional projects, then while you are in the sharing tab, you can deselect the projects where the user does not have Project Admin access. Please Note, that this action will un-share the page with any projects that you deselect and thus impact users in those projects. So a discussion would be helpful with other project admins and users - was the page shared with those other projects for a reason, do they use the page, impact if they don't have access to it, etc.
If you determine that the other projects need access to the page but you don't want to give the user Admin access to all of the projects, then a Workspace or Subscription admin will need to administer the page. Both of these Admin types have access to all projects in the workspace or subscription respectively.