I'm going to expose a sex worker at work
What good will exposing this sex worker do?
What do you think, what would you do if you find out your colleague dated a sex worker once every week.
When you meddle in other people's business, you are involving yourself in a situation where the outcome doesn't fall on you. You should instead keep their secret as it has nothing to do with you.
People should not be allowed to do what they want behinds our back. I was pissed when I found out that I bought alcohol for her.
This is still not really any of your business. You should allow your coworker to have their privacy since them dating a sex worker doesn't even affect you personally.