Sexual relationship with wife is near nonexistent

I'm so sorry you're going through this.

I had a virtually sexless marriage for many, many years, and it turned my relationship toxic, and caused my wife and I terrible amounts of pain. It took a long time to us to figure out I was a type of asexual and had, and would never have, any real interest in sex with anyone. Asexuality is an outside possibility you might want to be aware of (the AVEN website helped me consider that side to me).

I humbly suggest that it's better to get it sorted as soon as possible, and if necessary consider ending the relationship - the pain of a sexless marriage isn't worth it, IMHO.

To me this signals a major marital issue, one that could lead to separation.

Yes to the above.

Many centuries and thousands years ago in cultures where divorce generally was not an option, this situation still would have warranted a divorce. Have you voiced to her that if the situation does not improve for you, you would separate from her? If she hears it for real, she might change without your spending (and possibly wasting) money on therapy.