YABU, on the whole.
When you break up with someone, you have absolute no say in what they do or a right to be annoyed by it. It is literally nothing to do with you anymore (from the point your relationship ended until the point you got back together). You can’t criticise him because he hasn’t done anything wrong.
He didn’t “replace you”- although, even if he had, it’s not like he betrayed you in any way- he simply went on a date. It’s not like he proposed or suggested moving in with her. It is absolutely fine to go out on a date when newly single (e.g. if you meet someone you like). It can be a bit of a boost to go out and have fun with someone after a difficult break up. And in all honesty, most serious relationships don’t end because of a single argument, the argument might be the final straw or re catalyst, but usually not the sole cause. Perhaps he had begun to move on in his head in some ways already?
Alternatively, sometimes people do things that are somewhat out of character when they are hurt and upset- I have certainly done something on the rebound that I would not normally do. What timeframe would it have been “acceptable” for him to go out on a date?
I suspect you don’t like it because it hurts the ego a bit to realise he wasn’t sitting at home upset and pining for you (maybe you were doing so for him), but had tried to move on quite quickly. Are you worried that he isn’t really as committed to you as you would like him to be? Perhaps seeing his attempt to move on quickly as evidence of this-hence being upset/angry that he went on this date when he was a single man, fully entitled to do so).
I think he was a bit unkind to ghost this woman in the way he did. That said, it was one date, some overly enthusiastic messages and a bunch of flowers. Was it the most honourable way to behave? No. But it’s not like he led her on in order to jump into bed with her and then ghosted her once he had what he wanted. He should have let her know he was no longer interested and left it there.
I also thinks this woman does seem especially intense and hung up on him/what happened. I think it is quite unhealthy, actually- possibly even potentially quite creepy. I wonder if he picked up on an undercurrent of this, and did not know how to end it with her without ruffling feathers or causing drama. He should have just ended things with her, of course, but maybe he worried that she would blow up and contact you or would not take no for an answer/not leave him alone.
She does seem more than a little too interested in him after all this time. Tracking him/you down, sending those messages etc. What was she hoping to achieve? Nothing good, I’d wager. I think you need to consider her motivations too.
I don’t think any of us are perfect, we all make mistakes or poor choices, and do things we regret. Have you always behaved impeccably in every situation or relationship? I think that, whilst I would agree that he did not conduct himself perfectly towards this woman, it wasn’t a particularly significant misdemeanour either. He has not done anything wrong as far as your relationship goes- he didn’t cheat on you or betray you in any way. He acted like a single man at a time when he was, in fact, single. Ultimately, I think that unless you have other reasons to call his character into question, or given you other cause to doubt his sincerity or commitment to you, then I think you need to put it to bed and move forward. Or, if you don’t trust him or believe he is a good person- end the relationship and have done with it.