Adding to help those in the future finding this thread.

Supposedly extra tickets are made available about a week or so at the official site https://ticketing.colosseo.it/en/

The site is definitely swarmed by bots. Everything sells out at the initial 30 day window within seconds of release.

Following Reddit post describe how to increase the odds a bit - A Guide to Colosseum Full Experience Tickets. This saves you some mouse clicks and server/client website exchanges which could make the difference between getting tickets and not be able to get it.