In the short term, I understand its important to know exactly what happened. Betrayal comes with a need for the truth. So I would say, look at the evidence and decide what you believe
In the long term as everyone says it won't matter because you'll know he intended to and opened the door to it and having been through this it'll eat you alive from the inside.
I won't tell you what to do, but knowing he did that won't ever go away. So it's up to you to decide if you can live with a partner who flirts, texts and is open to sex with other women.
I think cheating can sometimes happen due to circumstances. Lots of alcohol. Business trips. Getting to friendly with someone and a line gets crossed.
But this is different. He'd carried on texting her. He was getting a thrill and that just means he'll always do that. When you're older or sick or something, he'll be off with some floozy.
If you can live with that pain, he might stay with you or he might upgrade you. Sorry to be blunt but it isn't about you. Men like this might love you, but they can't BE loving.
They want to feed their ego, get admired. It's shallow and very weak. Some people marry and live with men like that and are relatively happy.
It's not impossible he can change, but to do so, you'd need to do huge work and he'd need at least 12 sessions of counselling to understand his character weaknesses and possibly fix them.
Don't be suprised if he's not interested in doing that though. He's got a character flaw darling. Some people do.