I figured it out. Because I have the Project license that permits Project Online features and functions (Plan 3), I am able to access and interact with other people's projects even though I am not a member of their group. We have an old PWA site collection and a few people with the Project licenses (don't know what their license level is though) who have 'played' with the app but because it requires all the group members to pay for a Plan 1 license at least, the users did not continue using the app and did not delete what they'd created. As a result, there were a few past projects listed (the old PWA) and few new abandoned ones (Project for the Web).
I didn't know that having a Project Plan 3 license not only gives you admin level access to the old PWA sites but also gives you access to the new Project for the Web projects for which you have no affiliation nor do you want it. Not the functionality I expected, obviously. Really through me off!
