I'm old and cantankerous, with the hide of a rhino and have been though narcissistic behaviour and been burned by it more than once and now recognise it on sight.
Red flags and alarms are going off in my head when I hear what you describe. Your feelings are valid. Your jealousy is justified. Trust your instincts.
If he loves you and is committed to you he will care deeply about how you feel and how his behaviour makes you feel and want to change.
If the fling truly didn't mean that much to him it would be a no-brainer to prioritise you and stop the texting. Why does he feel the need to keep texting her, to the point where he knows it's hurting you but still does it?
Because you're being emotionally manipulated and controlled and set up for his cheating later.
Maybe he won't with this woman (because it doesn't sound like she's up for it), but with another at some point and I am willing to bet good money on the fact that this is what he's done in previous relationships as well.
He's afraid of being alone so he will stick in a relationship until he finds the next best thing.
Anyone who very deliberately tells you that "they hate cheating" is setting you up. When you suspect or find him cheating he will entirely blame you for it. He'll say you're paranoid and suspicious. He'll say you "drove him to it". He is laying the groundwork for it in your head now.
"It’s also how it makes me feel — like I’m jealous and controlling even though I’m not" - be reassured that you're not, but that's the way he wants you to feel so that he can blame you for what he's doing. He is deliberately making you feel that way so he can keep you under control.
Darling, when someone reveals who they truly are believe them the first time. He sounds very much like a narcissist. You deserve better than that. In fact, I'd run a mile. You're not mourning him or afraid of losing him. You're afraid of being alone and mourning who you want him to be, who you thought he was.