I would like to say - that I think 'outing' the affair is absolutely fine - and often to be recommended.
The minimum consideration is to tell the other BS. (with the proviso of ensuring you and children are safe and ok in this). The other betrayed spouse always has a right to know. And although it is a very personal and difficult choice (and I am very supportive of taking care of yourself first and making sure you are ok).
I don't think it is revenge to also disclose any illegal, unethical or corrupt behavior and actions undertaken in the name of the affair.
Especially if this helps for no contact to be maintained.
A condition of beginning our journey of healing and a part of disclosure was that my spouse had to call his managers and disclose the affair and acknowledge how it had effected his work performance and his less than proper use of work resources. This is what was right for us. Because we needed time off and flexibility to access our therapy appointments and manage my trauma and his depression.
Anyway I digress. Disclosure, transparency are necessary for the healing journey.
It helped to build our trust as well.
Disclosure comes with risks that need to be weighed up by each one of us.