Welcome here, little sister...
It's perfectly normal to feel upset, frustrated and confused by all of this. The number one rule around here is to take care of yourself and your health so that you can be at your best for whatever the future brings.
Affairs happen when a partner refuses to deal with problems and their own internal insecurities. It is what makes the external validation so attractive which then leads down that slippery slope.
You may or may not have had issues in your marriage. WS's like to claim this because they do not want to be responsible for such assoholic choices. Even if there were, he should have been discussing them with you. Usually however, it is the spouse that contributes less to the marriage that takes on such selfish and destructive behaviour. Even if there were issues, having an affair is like burning down the house to fix a leaking pipe. In no way does that choice make good sense.
Your WH appears to be taking some positive steps forward for reconciling with cutting of contact, accepting counseling, and being truthful about the possible STD. There is still much for him to do as it requires him taking full responsibility for his choices (without blameshifting) and actively working on making amends to the marriage. All you can do at this point is to express your needs and boundaries, and look for consistency of his action over the long term.
Whatever happens though, if you can commit to your healing and be willing to look out for your needs and stand up against what you won't tolerate, you will move forward with your life. It's gonna be tough... it's gonna hurt like hell... and it's gonna take time and effort, but if you can value and respect and honour the person you are, you will be okay.