All these people with wild theories, are you script writers for the soaps.
The guy made a mistake, and couldn't live with that mistake so admitted the truth.
His alternative was to not say anything and eventually jump from the bridge.
He hasn't pressurised the OP at all
Op, my initial advice, as from reading your posts it reads you would like to make the marriage work, start counselling and talk through this issue, and other issues there may be.
Only you know your husband,no one on this thread does, yet they all act like judge and jury.
If you believe what he says, that is what matters,not what some random tells you you should think.
Do your husband not have a mate he could stay with for a few days, or could he stay with your parents, to give you some space. This is allowed during covid restrictions.
If you do want to try and fix this, don't listen to all the conspiracy theories from the soap writers on here, listen to your heart, your head, and what he says
If you believe he is being truthful, then it's up to you to decide if you can forgive him. It is possible to forgive him and continue with a happy marriage.
If you can't forgive him, then end things, amicably if you can, it would be better for the kids if the parents that split were friends rather than enemies.
I would do counselling together as this will help you make a decision