I live in Spain. Entry requirements for vaccinated individuals are basically just fill out the form. They are generally accepting US CDC card but it's up to each airline to enforce. Portugal is supposedly much stricter but I have my US vaccination validated in Spain for a certificate from Madrid.
Within Spain nobody will ask for proof of vaccination, masks are required indoors until next Wednesday the 20th when it will only be required on public transport and elderly homes. Lots of people saying they will be masking more at that point but curious to see how it will actually work out. (I'm flying out the day before so won't see it) When going out to bars and nightlife, nobody seems to care too much.