DID HE CHEAT OR NOT?

pls i need to know this because my situation is complex and it bothers me.

I got into this relationship knowing full well that my bf wasnt over his ex-bf. I was okay cus like alright he can ger over him soon right!? its just rn i find it weird that his ex-bf back then always get in contact with him after i had him changed his numbers, delete his socmeds and make new ones under a fake name, like i did for close friends only. i always thought that "oh hes fuckint obsessed thats creepy" but uhm... just weeks ago i logged into his snapchat and i saw that he and his ex were still friends there. I didnt bother to look at the messages cause respect ahahaha after all i only logged into his acc to get some pictures.

he opened up to me or well more of so that i found out from someone that his ex was like s*xually harassing him and bothering my bf. So i was like "oh okay he didnt cheat" but i know how men are like some of them dont take a no for an answer and so i excused it cus ig he got harassed by him but its just some other things dont match with me. Before i found out about this I confronted him about his ex dming him still he was like "i feel sorry for him" i understood cus he was the type of ppl to have alot of empathy and i told him to just block block. dont feel sorry. then now the snapchat, he didnt lose full contact with him. He was talking with his ex behind my back all this time after i told him to cut contact but at the same time i feel sorry cus he cant say no but keeping this a secret from me?

TLDR: obsessive ex was still in contact with my bf even after i told my bf to stop contacting him cus all his ex-bf is harass him.