Is my boyfriend planning on leaving me for his ex?

We’ve been dating 8 months and share an apartment together. The lease is up soon. Today I was on his computer and his IG was open.. i opened his messages and saw some from a private account of a girl who’s icon is of her body wearing skimpy clothing. He’s the only follower on the account. There’s 20 posts. She has another public acct he follows too. They dated a year ago. She messaged him that she wanted to see him again, the door is open with a wink, and he responded he’s in a relationship but he still sometimes thinks of her and fantasizes about her with a sad face. She said she does the same, and he responded that he will keep that in mind, then asked her if she’d only message him during work hours to avoid drama and trouble with me and apologized for the request. She said that’s fine and then responded to his keep that in mind “please do keep that in mind” and he said “will do” with a smiley and wished her a nice weekend.

This is cheating right? Does he still have feelings for her? He’s been following this private account for 2 months now.. when I first noticed it I thought it was a fake account. Now I see it isn’t.

Is my boyfriend planning on leaving me for his ex?
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