Based on my circle of friends who are about the same age as you, your situation is more common than you might think. Everything OK in the marriage otherwise except the wife's interest in sex went from normal to zero over a period of years which, not entirely by coincidence, just so happens to be the period of years around perimenopause and menopause. This doesn't happen to all women entering menopause, but for too many the loss appears to be so gradual and so complete that by the time 20 years have passed, they are not no longer interested, they don't even want to be interested, and they don't even see the point in wanting to want to have sex. Which leaves them entirely unmotivated to go to therapy for it, go through doctor and hormone treatments, all of which they see as a huge waste of time and money at that point. Because they no longer even see the point of it, some of these women see a man's continued desire for sex as irrational and selfish, not to mention being a completely unconstructive waste of time. They only thing they understand is that, for some reason, if they went through the motions, the husband would be happy.
Not to mention that in menopause sex can be painful. So add lack of desire in the first place to pain and you've got a situation which is guaranteed no sex. So it's easy for these women to reason that if a man wants to "get off" why can't he just handle it by himself without causing so much trouble and wanting his wife involved.? Given all the men doing porn even when they have an attractive girlfriend or wife who is willing to have sex, why can't a man just be happy with porn if his wife is NOT interested?

It might not suit what you want, but may I suggest that you ask your wife, "If you aren't interested in sex at all and it's not important to you, then can I assume it's not important that I have that unimportant activity with a friend with benefits", or something like that. Just as a test statement, it might wake up your wife, even if you never intended to act on it.

You say she won't go to a doctor. What about a therapist? I'd try that first. If not, then perhaps ask her something like what I suggested above, or something along the general lines of having an open marriage. That does wake up some women.

I do wish more therapists wrote about this intractable problem. Too often I see advice columns which suggest there's a quick fix for lack of desire in menopause, and that's not at all what I've seen in real life.