I may be totally off base with this but I can't help thinking that your "enoughness" is perhaps a sort of side issue. With all the serious, somewhat scary,emotional and physical health things your wife has going on right now she may not be in a position to gauge what she wants or needs. You might want to try to set it aside for now as you may be torturing yourself over a will-o-wisp.
CFT, I had that feeling as well. Like you still concentrate on polyamory after several months, but this is not the major problem. It took half the discussion before you mentioned the dependent state, in which your wife is now, which seems odd to me.
...For me, relationships are about
sharing myself with others and other people
sharing themselves with me. I'm not filling needs or holes with people. I'm just sharing with them. It just so happens that I like to share with many and you prefer to share with one

I don't need to share sexual and emotional intimacy with
anyone but I chose to share either/both with people whom I connect with and I don't wish to have a limit set on a relationship before I even start it.
ETA: that last line and also that I do acknowledge that people sometimes use poly to fill that void...just as they do alcohol, escapism, etc, etc.
I love this approach, thank you for writing it. I want to be in relationships to share. Although I aknowledge that I DO need people to meet my emotional needs. Even the need for intimacy, and I do think that relating and sharing is a basic need as well. What you say is kind of and ideal, which is worth working towards for me, to relate because you want to share and cooperate, not because you need that particular person to fill something else.
...I feel bad for you because you define yourself in terms of others. You base your entire self worth on whether you are "enough" for somebody? I cannot even fathom living like that...
Vinsanity, sorry to say, but I think you are being overly harsh on CFT. Like you are comming from the other side, but with a similar level of misunderstanding. I agree that it is not good to derive one's self worth from other people. But I don't think this is the case here. Perhaps to some degree, but not as much as you suggest. His reasons for not wanting polyamory are different, and different then your reasons were.
Like I said, I'm not expecting the non-polys to get where I'm coming from. This isn't about some uber dependent personality trait that I have, it's about keeping what's special between us, between US. Me not wanting her to sleep with another guy is not caused because I feel she might like him better, or that she'll choose to stay with him instead, it's about cheapening what we have, by giving it so easily away to someone else. There's no such thing as "just sex" once you get to a certain point, and the life that we've built, is far too important to just do the same with another person... Especially one that you've never even met face to face. It's as though I'm being viewed in the same light as someone only seen on a computer screen.
There are a lot of assumptions in this post, that strike me.
"easily"? maybe what you view as easy, is not without a deep reason for her.
"No such thing as just sex?" I agree and disagree, since some people can keep relationships without going up the relationship escalator. Did she say wants to build a life with him? Or does she want to keep "lives" separate and just share moments of it? Does she want to build life with both?
"being viewed in the same light as someone only seen on a computer screen." This, too, is an interpretation.
I think you might want to focus more on behavior, than on feelings. Thinking "if she rushes to the screen every time instead of spending time with me, I don't feel valued" is a good starting point for work, and very different from "she likes the other person on the screen, so she doesn't value me".
Also I thought about your situation the other day and one more parallel crossed my mind. When I was in love with my current poly partner, whom I barely knew at that time, and was deciding what to do with it and with my monogamous relationship, I told my psychiatrist about my struggles. He is wise man, and he asked what was so important about that poly man. I gave it a thought and I said: He listened to me. The psychiatrist went like: Wait a minute, WHAT did he listen to? Because that is, what is really important.
After time has passed, I really agree with the psychiatrist.
For me, it was the longing for a certain kind of intimacy. Also for more freedom and openness to be intimate with others. Also, he listened to my pain, and he didn't mind. He accepted me with my depression as being part of me, offering useful feedback to work on it, but not trying to "cure" me from my illness.
This will be probably in line with your perception of the primary relationship "not being enough". I will not dement that, but from my experience I want to make two points.
First, it was not about my partner, it was solely about ME, my needs and my shortcomings. I actually think "being in love" (not loving someone in a true stable sense), that crazy feeling, is always about that to some degree at least. My partner at that time was actually great in many different ways, we had a great intellectual connection, and emotional understanding as well, common goals, we were a good match to cooperate. I find that love is blind to that, it is about unmet needs, but it disregards those which are
being met. Me falling in love was in no way my partners "fault". Also, if I knew about my needs, my partner could have perhaps met some of them (with a lot of work together), but certainly not all of them.
Second, I think it might be really important to find out what was important to your wife about her online relationship. Finding alternate ways to fill that might be the necessary change your relationship, even the way out of her depression. Also, listening to that in a kind non-judgemental way, if you are able - very healing to her. (But it sound like perhaps you cannot and she cannot speak, so that would be work for her therapist then

.)
However, from my end, I just don't view adding others into the bedroom as allowing happiness. For me, to do so is to add pain, misery and agony. And for her to be "okay" with something that hits me over the head with something that creates such negative emotions, well, she might as well be telling me she hates me.
I am sorry for that. But again, her wish is not about you. Repeat. It is her wish. The wish is to be physical with another, not to hurt you.
It is an unnatural concept to most, but I firmly believe, that if you are hurt by another persons wish or feeling, it is your reaction and your responsibility, yourself hurting you, not the wish itself. That doesn't mean you have to accept whatever behavior, it just means, she is not a bad person for having a wish.
Besides, you said she didn't actually ask to open up. Why did she not ask or act? Perhaps she cares about your negative emotions.
...It tells me, essentially, "I want to sleep with someone who isn't you". In other words, "there are times when I don't want you."
This might be the case, but those two statements are not the same. She wants to sleep with someone else. That is all, really. It tells you, that there are times, her favorite activity would be to sleep with someone else. You are probably not surprised by the fact, that sometimes she chooses to do other things, then be with you - after all, she has friends and hobbies, no?
...
She fell for someone else. If that means she is finding out she doesn't want you? Well, that is a good reason to be depressed, if a long (and perhaps somewhat codependent) marriage is to end. Sorry, that this is an option.
If that means she wants both? And she knows it is impossible with you? A good reason to be depressed again, if she has to choose, and both options are a loss.
If that means she doesn't actually want that particular person, but certain missing peeces? Find those.
I am very much hoping, you overcome this successfully, whichever that means for you.