How to look at my bf(25m) who attempted to cheat on me (25f) in an emotional affair?

This is a throwaway account because he knows my main account .

So a month ago my bf(25m) told me he decided to reach out to an old flame from high school to update each other on life. He’d said they didn’t date properly back then, and had a friendship going on as well. At first I told him I find this very bizarre. We’ve been together for 5 years and we have a 15 month old son and nothing like this ever happened.
He assured me it’s just old friends rekindling so I didn’t give it much of a thought.

Fast forward to now, a month later. During this whole time they were texting obsessively every other day, sometimes all night long.
I’ve read the chat at some point because I got suspicious and there wasn’t anything straight up crazy but subtle things that I can tell sound like flirting. He was complimenting her all the time and patronising her. Saying things like ” oh I wish things were different back then,I would’ve done better with you” or telling her he’d buy her three Tiffany rings while I’m waiting for an engagement for awhile.

He started insisting that we all meet up with her, but the weekend he chose I was busy with our son.
To my utter surprise, he got into a huge fight with me right before, and went on alone to visit her. He dressed up in a suit which is rare and he spent 10 hours at her city.

When he came back, I confronted him, he obviously refused that he is cheating and said he never slept with her. However in my opinion emotional affairs also exists and this pretty much fits the description.

After some back and forth arguing he admitted he has some feelings for her and that the reason for his trip was to “confirm things”. I told him I’m leaving him and I was pretty serious about it, he seemed fine and even discussed it calmly. Next thing I know, a few hours later on the same day, he comes back from somewhere, falls in my knees and starts telling how big of a mistake he made, how much he regrets it, that we should marry, proposing to me (without a ring).

In his opinion, I’ve had such mature, loving and respectful conversation with him during the breakup discussion like we haven’t talked like this for a long time. For me personally it was more of a be respectful thing because we share a son and 5 years behind our backs.

My response to all of this craziness was no, I don’t buy it. I found out that in these few hours between the polar switch, he had spoken to her, kind of admitting his attraction but she cut him off.
Now he is all into making this work, “it will never happen again, it never happened before”. He said he was missing nurturing.

I will admit that our relationship has been extremely rocky and unsettling since we became parents. He lost his job a year ago, lost his visa status, is constantly stressed about money and future while I work part time. For info he pays rent and utility bills with some inheritance he has.
Some friends suggested me that because of his life circumstances and desperation he’s hit rock bottom and lost it, that’s why he did this stupid sh. But I’m so confused right now, how to look at him. And even if I do look at him it’s hard to understand what’s up.