Is it wrong I talk to my ex?

So me and my ex broke up about a year ago now because we just weren’t compatible she was a extrovert and wanted to have a large amount of friends and wanted to go out all the time. While I on the other hand am a introvert I prefer a quiet night in and I couldn’t really afford to take her out all the time. So you see we could easily fight and one of the reasons we got together was probably we were both in the same group and came out at the same time. So we fought a lot but we were both mature at the end of the day and decided to break it of before we started to hate each other. Now I don’t have feelings for her anymore but I still care about her since she’s my friend.

About 4 months I started dating again and my friend was incredibly supportive and I found my amazing girlfriend. she likes to stay in and is confident and we both love to Netflix and chill more then a fancy dinner. Amazing right I finally found someone I’m compatible with well... then I introduced her to my friends and my ex is in that group and that’s when I realised that I’m obviously making my girlfriend uncomfortable. I understand it’s an uncomfortable situation to be in for anyone so I told her that if she really doesn’t want me to hangout with her then I wouldn’t do it one on one but with the group instead.

Me and my girlfriend had been dating for 5 months when we fought about my ex. We usually don’t bring up the subject since it’s sensitive on both parts but one day my ex called me crying saying that her and my girlfriend had a fight. I asked what happened and she told me that she was on a shopping trip with the squad (I hate that I just said that) for my birthday and they ran into my girlfriend and her squad (oh and again) they wanted to buddy up. She said she doesn’t know how but her and my girlfriend started talking and it got on to my birthday. My ex asked if we were doing anything special. My girlfriend mentioned that she was meeting my family for the first time (bad idea turns out they don’t like her as much as my ex) my ex trying to ease the tension started giving her tips on what to do with my mum and dad. My girlfriend went

“ well sweetie they might have changed since you last saw them or any parents in fact since your dates only show up once and then dump you after you suck their dick”

Which was a jab at he ex boyfriend who was a douche. Still she smiled through it and bit her tongue. She still wanted to talk so she started asking my girlfriends squad what they were getting me and they said they were looking now. So my ex started recommending stuff I’d talked about a couple weeks before. Then my girlfriend went

“Could you shut up about MY girlfriend what are you like obsessed with her. She doesn’t want to date you and probably only hangs out with you out of pity”

And before you say I’m only listening to my ex’s side but I called my friends and my girlfriends friends to ask what happened they all said what I just told you

I don’t know what to do. I’ve known my ex since nursery and I had genuine feelings for my girlfriend but all her possessiveness and jealousy has put me off a bit.

What do I do?