Hey Papoi!
So to trigger the Petra storyline, you need to catch Xavier and transform him, then talk to him in his new place at least once. Once you're able to be intimate with Petra and have caught him, you should be interrupted in the middle of the night by your favorite security chief.
If you've done both of those and a week passes without Petra showing up, let me know, we'll coordinate getting save data over to me and I'll make sure we didn't break something.