I am also curious to see how the rules in Italy (and other popular tourist destinations in the EU) evolve. Here in the UAE there is another permutation in all this where many of us got two doses of Sinopharm early in 2021 and then two doses of Pfizer six months later. My vaccination certificate (including the one in the TousAntiCovid app for France) shows 4/4 doses - most people in Europe were pretty shocked when I showed them the certificate last August already.
As per UAE govt rules, those who have had two Sino + two Pfizer shots cannot get a fifth shot of any make (Sino / Pfizer / Sptunik / the new Sinopharm) which will leave quite a few people SOL. The official reason given is contraindications when administering a "fifth" dose (depends on whether you recognize Sinopharm or not).
Given the trip I'm planning for May I do hope that the rules are further clarified for cases where the booster was administered more than 270 days earlier.
Ro