Should i break up

We live together and recently i saw that his ex of 10 years ago reached out to him on Instagram. The last time he spoke to her was 3 years ago before we met. This is an ex that he told me was very toxic and abusive (supposedly). I was using google on his phone when i saw the notification and he was surprised. He texted her back and they had a conversation like asking how her kids are doing etc. She shared her phone number and they started texting on phone. I don't see any flirtyness or inappropriate things but he never told her he's in a relationship and living with me. She's constantly complaining and venting to him about her failed relationships and baby daddy etc. She brings up memories they had together, like a joint they smoked one time or that time she had a bad time or that time she cooked this and that. And telling him to make sure he brings breakfast for work and him responding: youre babying me". I dont feel comfortable. I saw that he was texting her the whole day while he was at work, from the time he woke up 6am to the time he came home 6:30 pm. And he only called me like for 20 mins to speak and barely texts me. Which bothered me. He noticed that my energy is off and i told him i didn't want him to talk to her and he said okay and he's still talking to her. So now he said he's going to change his passcode and everything so i leave him alone. I feel like i need to break up and it hurts because i dont want to. I mean, an ex is an ex for a reason and the fact hes not prioritizing our relationship and not respecting my feelings it hurt, i dont know how to break up if we are living together. I feel like he cares more about this ex. Ik its wrong to look into peoples phones but i feel it in my gut that it's not innocent.