I’m sorry about everything you’re going through right now and wanted to add an additional thought on telling your kids.
Give some thought not only to when / how to tell them (you’ve gotten some great advice already), but also to what their reactions might be in the days / weeks / months after and how best you can support them. When I went through this with my young adult kids, I was open with them that for my own wellbeing, I needed to have minimal / no contact with their dad. I also explained that they each might have a variety of reactions, from wanting to maintain a relationship with their dad to NOT wanting a continued relationship with him…or things in between…and that their desire to have or not have contact with their dad could change over time.
Most importantly, I was open about the fact that each of us might make different choices. One kid might want to maintain a relationship with him and another might never want to see him again. And all of those choices are valid and ok…and we need to respect and support each other’s choices. The kids and I had a lot of conversations about how they were feeling with respect to their dad, for months after the affair was exposed, and I think that was a good thing.
I’m sure you don’t want any tension or rift happening between your kids if, for example, one wants to be very supportive of your wife while another is angry / doesn’t want to talk to her. One kid might find her suicide attempt emotionally unmooring and not be so focused on the affair, while another may be distraught about the affair and shrug off the suicide attempt. One of the kids deep down may want to find a way forward with his / her mom but also feel torn about being "disloyal" to you. It can get complicated and messy, fast.
Your wife may feel that the kids are adults and will be fine, but there is a web of relationships between all of you, and the change in the relationship between you and your wife will have an impact on all of those other relationships. Unfortunately I don’t think there is any way around that, so the best I can offer is to acknowledge this with your kids and invite them to share whatever is on their minds. They are adults, but they are still humans, and this news will still forever alter their sense of "family" and "parents". So talk, check in, stay connected, encourage them to talk to a therapist or trusted person, etc. and all of you will get through this, together.