Upvote:3
Now, for personal reasons, we planned a trip to Greece and Italy in June, just a few days after her student visa expires. That's the first problem. But I was researching and it seems that with her American passport, she can legally enter Spain, Greece, and Italy on tourist terms, which seems perfect. Is this correct?
Yes, see How to switch from Resident visa to Tourist visa status in the Schengen area? and related questions.
Then, researching and thinking a lot about this, my partner recalled that Europe banned US travelers because of COVID-19. So, if instead of having a valid student visa, she is planning to use her American passport instead, the ban would apply to her? I mean, she is already in the EU. Does the ban apply to her case?
One thing that hasn't changed since last Spring is that US citizens residing in the US are not allowed to come to Europe for tourism. That rule doesn't prevent a US citizen residing in Europe from coming back from outside Europe nor does it apply to US citizens already in Europe.
Many countries have, at one time or another, imposed additional restrictions, including on EU citizens. This could prevent travel between countries, even for you as a Spaniard or for US citizens with a valid residence permit. In my (limited) experience, enforcement focuses on travel purpose and other restrictions (PCR test), the expired residence permit wouldn't make a big difference.
May is still some time away by current standards so it remains to be seen what the exact restrictions are going to be.