I believe that most people should leave their cheating spouse. I believe it even more so when there are no kids, because you can go full NC, which helps in healing. When I was first going through this, I read dozens of books on infidelity, brain function, narcissists, etc., and it was pretty clear that people can't really change who they are. Had you asked me even 1 month before D-Day, I would have told you my WXH was my best friend, we were the perfect couple everyone envied, etc.
I was 33 at D-Day, he'd been my only, I'd just put him through med school/residency/fellowship, we traveled to Europe 3-4 times a year, volunteered together, and life was looking amazing. We did everything together, he was my best friend, and I was so in love with him. We were CFBC (he'd also had vasectomy), no money problems, pretty much never fought. Life was perfect.
And then he cheated, because that's who he is. He tried to manage his impulses, but he only could for 13 years. Your husband is a cheater. It is very likely that he will cheat again. You set yourself up for much greater happiness by finding it now and leaving the cheater, then dealing with another D-Day 1, 5, 20 years down the road.
For me, I spent about 4 years dating casually, made a ton of friends, and made a great life for myself. When I wasn't looking, I met the man who has been my SO for the past nearly 5 years. Things are so much better with him than they ever were with my WXH. I had no idea life could be so great! Cheaters usually have other unpleasant personality traits (otherwise they wouldn't have it in them to cheat), that I just didn't see at the time, but being with a man who truly values me, who has never cheated in a relationship, and is a giver instead of a taker (we both are givers) is revelatory.
It's your life. Lots of people disagree with me, especially on SI. The best advice I received was on a different forum where a posted told me "you are the parent of your future self" - it really made me think. What would I tell a friend in my situation. What did I want my life to look like in 5 years? My WXH wanted to reconcile. It was so hard to say no. I still loved him the day I divorced. But it's the best thing I could ever have done.
Best of luck to you as you make this decision. It super sucks that he put you in this position. Please take care of yourself, get tested for STDs, drink water, and put yourself first.