You found out the stuff that most people here don't get a chance.
Most people here, the cheater already deleted the evidence, and the cheater gives the same line you did, but the same stuff happens a lot. Your situation is not out of the range.
She enjoyed the sex. Sex is 90% mental, and she was excited by the secrecy, she was excited by the fact that this guy desired her, desire is a big deal, and her being younger.
I had thought it may have been AM or Facebook because (1) he was wearing a cap in the video, something a younger guy does and (2) you saying he was younger and (3) her mentioning going on sabbatical, which she wouldn't need to if it was a co-worker, and (4) when you confronted, she immediately mentioned deleting social media.
The fact that she sought AM in my opinion makes it more difficult to reconcile, in my opinion makes her being further detached and ready to move on, and in my opinion more likely to go underground or just wait a while to find another player.
1. Did they talk about "love" each other?
2. What did she say about you to other man?
3. Did other man goad her into saying about you, or did she initiate it without him saying anything?
4. How long ago did this start?
Based on the toothbrush comment in the video, you said that your wife said that without the other man asking for it. That, to me, tells your wife that she is very, very angry about you, and/or extremely resentful about you. If she did stay with you, I would suspect she could easily cry about how sorry she is and then turn around and continue stabbing you in the back, because in her mind, she deserves it, and you deserve for being such a bad husband. Typically in this situation I've seen that the wife thought their husband was all of the problems in their life, and none of their unhappiness is any of their problems. They never consider how the husband is. Selfish, greedy, me, me, me. If that is the case, even before you discovered the infidelity, you should have seen that aspect of her selfishness; at the very least, you should be able to see it now in retrospect - if that is her type of cheater.
The fact that she sought AM, followed through, loved it, and had no indication of stopping, as matter the opposite, seemed she was getting even more into it (as an example, started a sabbatical so she could get more sex action), would tell you that when she immediately said how sorry she was, would show that it was a lie. Add that to the fact that she wouldn't tell the other man's name. Her saying she was sorry and it was ending very, very likely was just a lie.
Filing for divorce, full custody, that is what you should have done no matter as long as she was not showing you any ACTIONS.
You should continue the other actions. Tell the other man's wife, don't give her cruelly details, but give her enough that she knows it is true. Offer to give her some a little bit of evidence.
Tell wife what you want to about the divorce, I personally would stay silent and let her find out when served. Meantime, move her stuff into a separate bedroom, a basement, etc. Tell her to give you the handwritten no contact to the other man, also to the toxic friend. Very likely, the toxic friend also is in affair with AM, so let the toxic friend's husband what is going on, also.
What I am saying is to kill the affair anyway, even if you think you will divorce. You don't want this guy in your wife's life, even if she becomes an ex-wife, you don't want this guy being around your kids, deal with him, etc. So blow that affair up, too, even if you are divorcing.