Boyfriend hasn't cheated (yet) but probably wanted to do it anyway

So I (35F) found out today that my boyfriend (31M) of 9 months has been on dating apps the whole time we dated. In the past 2-3 months the conversations became more frequent and even went on multiple dates with someone who he's been talking to for months. I confronted him, he insisted nothing happened, then just talked and had drinks. The girl broke it off eventually.

Even if I believe that he hasn't cheated on me, just talked to these girls I can't help but think it was just matter of time. He works as a bartender btw. He said he loved me, he wanted to be in a long term committed relationship with me from the beginning. He has a very bad relationship history, he has been cheated on and he says he has commitment issues, he knows he shouldn't do but needs this type of excitement (talking to new girls).

He said he will go to therapy, he'll quit his bartending job and do everything to earn back my trust. I just don't know if I can look past this, was our whole relationship is a lie?

TL;DR my boyfriend has been talking/meeting girls almost in our whole relationships, says he didn't cheat and goes therapy to work on his commitment issues. Should I believe him?