Oh op, this has been going on for 4 months now, 4 months of misery and upset all on you, caused by him. Please just put yourself first.
This reminds me very much of my dads affair, only ever apologised to us once and then expected us all to carry on as normal and forgive. Said he wasn't in contact with her anymore but he was - played my mum like a fool in all honesty.
This was years ago and I'm still close to my dad though I'm sure he still feels no remorse for what he put my mum or anyone else through.
Imo, you can tell if someone is sorry, really does feel guilty after an affair - and affairs for me can mean anything. Texting when you shouldn't is cheating. Having to hide/delete things from your phone is cheating.
He doesn't sound sorry/guilty/ op. He should be begging for forgiveness. He should even be leaving his job to get away from this woman.
I don't think this man has any ounce of decency in his body and you most definitely do not deserve anymore of his crap.
I hope you find the strength to move on from this - my mum did. She saw my dad was still messing her about and ended up. Fast forward to now (8 years later) she's happier than she was before. Probably too early for you to be thinking about the future but you can get through this and come out of the other side. He just needs to be put in his place and you are the only one that can do that. You just need to find the strength to do it x 