Is this cheating?

My bf and i had a huge fight and we decied to forgive each other.
I was trying to login to my insta from his phone when i saw a recently log in account that i didn't know of on his phone (yk how insta usually show a recently login account? And you can just tap it to relogin..)
so i check his DM and there it is.. he send a dm to his ex.. i mean that girl didn't even answer him (maybe blocked by her idk honestly i was too out of it when i found out)

They didn't talk, but i feel betrayed..
Not only he send her text asking for her well being, he also didn't deleted his chat history with her...