I'm not convinced that the vaxx has been fully approved.

Here's the actual letter from the FDA:

https://www.fda.gov/media/150386/download

It still talks about the EUA. The one section that is hanging everyone up is the one that mentions a biologics license application.

Here's what a "biologics license application is":

https://www.fda.gov/vaccines-blood-biologics/development-approval-process-cber/biologics-license-applications-bla-process-cber

It doesn't sound like a full FDA approval to me.