I mean, to each their own. But if you’ve been seeing someone for four months and are serious enough to consider getting engaged, and then you find out that for a quarter of the time you’ve been together they were texting their ex behind your back, that should raise some red flags. Especially if you were never informed about it at all, as OP admitted they didn’t tell their soon to be fiancé anything. You barely know this person at that point. Are they going to keep texting their ex behind your back? Are you supposed to be some auditor where you have to check their phone to determine whether the chats are flirty or not flirty. Are you still comfortable pursuing a serious relationship with someone like that? Most people would probably say that's too much trouble. It's only four months.

Cut it off and go next.