This morning, I fired up my Microsoft Edge browser to connect to my demo tenant for Project Online and access the OData feed URL.
After a few minutes ensuring I had the correct URL (and turning off my Insert key) for the odata feed, I was still unable to get the output in the browser that I expected. I should have seen a long list of XML output describing the tables I could use for reporting. What I got was an "HTTP 403 Error Microsoft Edge can't get to this page." Unless Project Online was completely down (unlikely), there was something else going on.
As a sanity check, I entered the URL for my tenant https://myPJOtenant.sharepoint.com/sites/pwa and was able to log in as the MOD Admin just fine.
That's when I discovered my problem - I was acting as delegate for a team member. OData was applying that security rather than my Admin security and would not let me connect.
I ended the delegate session, went back to my OData URL https://myPJOtenant.sharepoint.com/sites/pwa/_api/ProjectData, and I received the output I expected.
This is the same sort of thing that happens when I have a project open in Project Professional connected to Project Online and I act as delegate for a team member. When I get back to the project plan and attempt some action like Publish or Checkin, I get a message saying I don't have permissions or have lost access to PWA.