Christ, this sounds EXACTLY like my STBXH (note the EX!).
He pulled this crap on our first date. He sat scrolling through FB, going "I dated her for a while. And her. Oh I really liked this one, I wanted her to be my girlfriend, but her ex didn't like it" etc etc. He was 36 at the time.
He also talked ENDLESSLY about his estranged wife - looking back, he clearly wasn't over her.
I was extremely vulnerable, with rock-bottom self-esteem, having not long fled a highly violent relationship. Nowadays, I absolutely wouldn't put up with this shit.
Consequently, I never, ever trusted him. He was at the very least sexting the woman he "really liked" - I was pregnant at the time, I caught him out after a message from her popped up on his phone, and he lied to my face, trying to tell me there was no message 😑
The lack of trust ate away at me for 9 years, and I was constantly anxious whenever I saw him sat there texting.
My advice? Run. At best, he's an immature, insecure man-child with terrible boundaries. This won't get better.