Strictly speaking you don't need to - because the intent is clearly there on his part - but if you want to, you could certainly catfish him and see what he does.
But the fact that, while you gave small kids (which is a time when most people's sex lives take a bit of a dive) .. he goes looking for a sexual partner online, without even talking to you or trying to resolve/improve the issue. He's willing, in theory to risk your health, betray you etc. If you confront him he'll use the "just looking" line.
If you can't fish him and he responds, sexts, looks like he'll set up a meeting etc. What are you going to do?
If it's leave .... You'd need to know what you're going to do/how you're going to manage. Universal credit? Part Time work (you can get 85% of child paid, up to a cap, if you receive any UC, rent? What would you get in a y divorce settlement? Etc etc .
Maybe get your ducks in a row before you cat fish him and confirm he's a cheater and you're stuck having to leave without knowing what your plan is, and how you'll cope financially etc..
But, it is enough ok it's own tbh.
If you were caught doing it, do you think he'd stick around?