i (30m) feel like my bf (33m) cares more about his ex’s (33m) feelings than mine

my boyfriend (33m) and i (30m) have been exclusive for about six months and i was fully aware he still is friends with his ex (33m). they dated about three years ago for only 2 months (i still don’t know what was the reason for the break up) and have been friends ever since. my boyfriend has told me that this ex has crossed boundaries with the boyfriend he had before me and would get very touchy to get a rise out of him. i was okay with my bf and his ex communicating until he told me this.

i feel like my bf is constantly bringing up his ex and it makes me feel weird. the other day we were driving past the hospital where his ex works and was telling me about how he works there. thought it was random and weird so i didn’t say much. a few nights ago when my bf was drunk he told me that he was speaking with his ex about how much he loves me and whatnot.

on another occasion i saw a text on his phone that his ex sent saying “i love you papi”. my bf didn’t respond but when i later asked about it my bf said it was just friendly. still not really buying that.

supposedly the last time they hung out as friends was a month before we started talking.

this morning we woke up and he told me he had a weird dream about his two exes making out and was going to text his ex about it in a joking way. this sort of rubbed me the wrong way and i asked him why does it feel like his ex is his confidante or something

we’ve been arguing and i’ve basically asked him to stop talking to him and he told me “well im not gonna block him lol but i wont engage with him or be rude if i run into him in person”

this lowkey makes me feel like he cares more about his ex’s feelings. what should i do?

tl:dr my bf still speaks with his ex as “friends” and i’m not cool w it