Sigh. I'm sorry, my first H was like this. I left him in 2008, so texting wasn't quite what it is now, but he was always flirting, and a bit handsy with other women after he'd been drinking. That graduated to him staying over at a woman's flat after a night out, and many, many other dodgy things. We'd also been together for 20 years, with 2 kids. But after 4 years of feeling like you do, I did leave him. I honestly just couldn't take any more.
Happy to say, I am now with DH no2, and he is nothing like this, despite being far better looking!
I've no idea why 1st H was like this. We had a great life, regular sex etc, and he was hitting on women that weren't more attractive than me really. None of it made sense. I think it was his personality, because he has done the same in his relationships after me.
In your shoes, having been through my experiences, I wouldn't hesitate to leave. But, I know that you're doing this for the first time, and I'm sure you will plod along until you reach breaking point, and something snaps and you just realise you are worth so much more.
Please don't feel any guilt at checking his phone. It's HIS fault that you have been driven to this! I checked my 1st H phone, when he was passed out drunk, and found evidence that he was shagging my very best mate. I had every right to know that, and I don't feel a shred of guilt. When men lie and gaslight, we ARE driven to do things that are out of character. And in any case, when no one has anything to hide, phones aren't like secret diaries : me and DH use each others phones if they are closer to hand, because we have nothing to hide! In my opinion, people who guard their phones fiercely often have stuff on there that they don't want their partners to see - and that's a huge red flag.
I think you should get out more with your friends, go dancing, flirt a little yourself. That was the start of the end for my first marriage. It made me realise that the world is full of nice men, and I didn't have to stay tied to a man that was taking the absolute piss out of me.