Need advice. Boyfriends ex girlfriend/ old best friend messaging me

So not very long ago my bf took a break and while on this break he started talking to his ex who also was a very close friend of his. He claims the whole time they where just friends but he would message her every night “goodnight I hope you sleep well” and message her every morning good morning messages. She’d also send him selfies and he’d say wow you’re so beautiful. He told her he loved her a lot. He would also send her very sexual memes. This ex of his though has a bf and did at the time of our break as well. Before we went on this break he would always find tiny ways to compare me and her. Like how I should cut my hair and she has short hair or I should get my nipples pierced and she has hers. They also have so much in common more than him and I. When we got off our break I told him I did not feel comfortable with them continuing to talk and he cut it off. Now here is the weird thing. She has messaged me twice since then. The first time months ago begging for me to let them talk again because she misses him and wants her friend back and just a few days ago messaged me again saying hey just wanted to check in on you and see how you guys are doing. Is that okay? Is it just me or is that weird? Like I don’t even know what to say. This girl gave me so much anxiety and made me doubt myself and my relationship sooo much. Why does she feel like she can still butt in whenever she wants? My boyfriend and I also have a daughter together and one on the way.