Hi, welcome to SI. So sorry you find yourself here, but there's a great deal of support among members who have walked in the infidelity shoes.
Why did she decide to tell the truth? Curious because cheaters rarely, if ever, tell the truth. Not only do they lie, they minimize their actions. Did the other guy's wife find out and threaten to contact you? Is it a work colleague?
Understand affairs don't happen in a a vacuum. There had to be some prior communication, texts, emails, flirting, etc.
Are you able to retrieve the messages from her phone with software? She should have been completely transparent instead of deleting everything. What was in those messages?
Your story is a bit similar to mine except I found out and confronted both my husband and his affair partner. Both of them told me they just kissed in the car which I soon found out was a lie. Husband on a business trip, they had prior communication before he arrived, she met him at his hotel, blah, blah, blah.
You have every right to snoop. Your wife lost her privacy when she decided to cheat. She needs to be an open book giving you access to her phone, emails, social media, etc. No compromise. When I found out about my husband's affair, he gave me access to everything and I knew exactly where he was and who he was with at all times. His work travel pretty much came to a screeching halt. I insisted he find another job because there was no way in hell I'd feel comfortable with him ever going to the OW site again, which was on the opposite coast. He stopped socializing on the job unless it was all men for lunch.
Honestly, I wouldn't contact the other man, he will only lie. I'd contact his wife with what little evidence you have. She deserves to know, and if you decide to go this route, don't tell your wife, the two of them will collaborate and make up some wild story like you are a crazy jealous husband.
I'd go into investigative mode and seek more answers if possible. Ask her if she's willing to take a lie detector test. Her words are meaningless, her actions will speak volumes. IMO there's more to the story, there usually is.
Please, please, don't sweep this under the rug. What is SHE doing to fix this hell she created? Did she inform this guy there is no more contact (in front of you).
Please seek individual counseling for yourself if possible. A nuclear bomb has just been dropped on your life, you need help to process the trauma. Check with your MD if you are having trouble sleeping or concentrating. Sometimes temporary medications help. Focus on you, exercise, eat healthy, lean on trusted family members and friends or a member of the clergy if you are so inclined.
Again, sorry you are now a member of the best club no one wants to join.