You don't have much proof. Basically what you have is circumstantial evidence.
The top sign of cheating is hiding/guarding the phone. Deleting texts. You've got that.
The second most common sign of cheating is changing in behavior. Cold, distant, emotionless, at best. Finding you annnoying, everything you say or do, literally sometimes just eating and breathing, annoys her about you. Obviously, she told I love you not in love with you out of the blue, she wants a separation out of the blue, no wanting to try marriage counseling first, you discovering messages that her friends are surprised your marriage is terrible (i.e., wife never complained about your marriage until now, when wife is ready to leave you and needs an explanation as to why) you finding an amusement park pic with another man which your wife would never keep from you something like that in the past, etc., etc., etc., a lot of circumstantial evidence. A story that doesn't make sense except if you imagine this whole cheating scenario.
You do know also that your wife has lied to you, deceived, and I am assuming, you can verify, she only deletes things about this other man, your wife is not normally a deleter of anything.
So you can be fairly assured that she is cheating on you as most of us would define cheating. Is it physical? Before I give my opinion, I would preface to say that cheating is a very predictable behavior. The cheater lies, deceives, guards the phone, deletes texts, blames the betrayed spouse even though in 16 years never had a real problem with it, wants to separate, I love you but not in love with you ... these are basic cheating behaviors that most "friend" affairs incllude - types of affairs with an ex-boyfriend, a co-worker, a neighbor, a teacher in the kid's school, a coach in the kid's sport team, a guy at the gym, etc.
In these cases, 98 percent it goes physical before the I love you but not in love with you and separation is rolled out. The denial of sex usually is after it goes physical in the affair. The cheater doesn't have desire for you, is getting it elsewhere, doesn't want to cheat on her other man - any number of reasons for that. As wife's friend said, wife needs to figure this out, needs space. Basically, wife has found another man who might make her happy like she's never been happy before, but she needs time to figure out what is best, new shiny or old reliable. New shiny looks really exiciting, butterflies in stomach effect gets her wetter than she's been in a long time, but what if new shiny isn't reliable, breaks down easily, turns out to be a lemon in the long haul. She'd like to get an extended test drive, not just the one hour at the dealer, but take it out for a week or two or month or two and see how new shiny really runs. If all is good, then she can get rid of old reliable, but not before. She still has some affection for old reliable, but she is really sick of the same old wear and tear, there has always been some faults in old reliable and sometimes you get annoyed with the little things that last a long time than a bigger issue in new shiny.
You may never know the full truth, but you can figure out that she didn't leave you without testing the other guy enough. I'd be shocked if she didn't have sex with him before telling you the I love you but not in love with you and asked for a separation.
As far as your wife and her friends being surprised. I think your wife's friends probably are moral, ethical people who look down upon cheating. They would not look well upon your wife if she cheated on you. So wife tells them the marriage is bad, has been bad, and she is getting support with another man, and she's starting to have feelings for him, and she can't help her feelings. She probably would lie to her friends, too, about the cheating if the friends disliked cheaters. My wife never told her friends she was cheating because they were against cheating. Frequently cheaters develop a new set of friends who are more amenable to cheating.
Your wife probably dislikes cheaters. Or she used to. And her and her friends were on the same value system. Now your wife is cheating, so she has to tell her friends that she separated first, then it really wasn't cheating. That would have been the next step, I guess. After she left that terrible marriage, this co-worker supported her and it turned to something else, something more.
Now from just the snippets you've caught there might be problems in paradise. Him telling her, you (wife) wanted a text, here it is, you must have fallen asleep, doesn't sound great. Wife got into this affair most likely because this dude was blowing smoke up her butt like 24/7, compliments up the gazoo, not I'm texting you because I have to because you said so, wife wants to hear from him I'm texting you because you are so hot and I am touching myself here and need to hear your voice you sexy thing.
Entrance wife's doubt, cue music of her wanting sex with you again to make sure her old reliable is still available in case new shiny turns out to be a lemon.