About the most official site ever of the Cenacolo, I don't get exactly if they have tweaked something recently, but the most functional site (in Italian and English) is https://cenacolovinciano.org/en/
The one of the Ministry is indeed official, but still just links to this site, and, most importantly, for some arcane reason its English version lacks this link (but has an email adress). I hope this site will remain stable for now. There are still some loops to go through to reach the ticketing site (Visit -> How to book -> licensee
link). For some reason, at the moment, availability seems to consider the current week only.