Ive seen many basements like that over the years. What is your goal for the space? How do you want to use it?

Your basement looks damp to me. Is it?

Making it actually livable may be a long and expensive undertaking.

If you just want to make it clean then yes, paint it. I have used products like this. It looks fine until the water inevitably gets to it.

Since you mentioned that your husband did powerwash it, I suggest you don't start with the upgrade until it's all fully dry and not damp. Water may ruin your paint. You can definitely paint the floor but I think it would look nicer and it will last longer if you choose a diff flooring or smoothen the concrete out first.