But is the pandemic over? It's clearly not, and that was the point of the lyric. Countries with 90%+ vaccination rates are still having lockdowns because of breakthrough cases.
Edit: and while we're here, here is politifact's take:
https://www.politifact.com/factchecks/2021/oct/14/joe-biden/...
Concluding it's "half true" fits this thread well :)
I say this as someone who's vaccinated; that is not true. It can limit the spread by reducing the viral load you give off, but you can still be vaccinated, get the virus, be asymptomatic (or not) and transmit it.