Living with an ex after break up

We broke up a month ago, and (24F) I’m in the process of moving out. I moved in with my ex (28M), lived together for 3 1/2 years.
It’s taking me some time to move out due to family arrangements and finding a place that allows cats. But even before breaking up I’ve been planning to move out to give our relationship some distance as we’re always together doing everything together.

ANW!!
Ex started talking to someone else at his workplace right after he broke it off. The break up is what we needed and I’m grateful it happened. But it hurts to think that he’s already getting to know someone despite everything and me still living in their house. I can’t fathom that she’s already sat on the passenger seat where I’ve sat on for years.
And recently he told me he has friends sleeping over, and those friends are friends with the girl he’s talking to. And he said he’s gonna introduce me as his roommate to make it less complicated..

Part of me wants to introduce myself as the ex to break off things with them or I don’t know create some distance LOL
Or just be okay with roommate cus we’re like roommates right now.

What do I do? 🤔 should I be chaotic? Or be chill
Cus why you such an avoidant— ofc I want him to be happy but this is like a slap in the face and feels like he doesn’t care how I’d feel?