@Biscuitsneaker I haven't read the whole thread but I have read all your comments and replies. Like other PPs I highly recommend you get some therapy for yourself if your wife won't go to couples therapy with you.
I am a therapist, so I'm obviously biased, but the difficulties you're describing are now ingrained and deep seated and are not going to be solved by love languages or trying to find ways to initiate that will somehow unlock the key to her missing desire. Your wife is giving you an impossible problem to solve and you're doing all the work trying to solve it. This relationship dynamic is part of the problem.
Relationship and sex therapists will see individuals as well and I'd recommend seeing a therapist who is trained in sex therapy as well as couples therapy, even if you are going by yourself. Not all therapy or therapists are equal and this is a specialist area. I say this because I'm not a couples or sex therapist, so I know what's in and out of my training and scope of therapy practice, and I would never offer relationship/sex therapy, and as a therapist I would never go for relationship/sex therapy with someone who wasn't specifically trained in it.
A therapist registered with the College of Sexual and Relationship Therapists would be ideal https://www.cosrt.org.uk/ but look at what training the therapist has done and ask about their approach.
I know that could feel like a big step so here some suggested reading and research material for you as food for thought. This all comes with the caveat that I'm an internet stranger and we really have no idea of what's going on in your relationship so the below information may be totally not what you're looking for.
Relationship therapy: read up about Gottman couples therapy and research, especially Gottman's "four horsemen" of dysfunctional relationships: criticism, contempt, defensiveness and stonewalling. These are communication styles that predict the end of a relationship. Your wife's eye rolling sounds like contempt, and her responses to you could be stonewalling. https://www.gottman.com/blog/the-four-horsemen-recognizing-criticism-contempt-defensiveness-and-stonewalling/
The Gottman methods are good for overall relationship health, as is another therapy method called Emotionally Focused Therapy (EFT), which is great for relationship problems where there is an anxious and avoidant attachment problem (note that anxious attachment is not the same as anxiety - I have anxiety but I tend towards an avoidant attachment).
However, I don't think Gottman and EFT therapy approaches are adequate for sexless relationships where this is has become a deeply ingrained problem. For a different approach Esther Perel is a relationship and sex therapist (she has a podcast called "Where should we begin" which has live therapy sessions with real couples). She is particularly good on relationships where the sex has died off, or there is emotional closeness but no sex (not sure if this describes you, but it doesn't sound like you have lots of open conflict and you and your wife get along, unless I missed something). She has a book called "Mating in Captivity" (I haven't read it but I have listened to her podcast and followed her work). Her approach is different because it's not about creating closeness and is more about what drives desire (some sense of mystery/unknown) and how to have that balanced with emotional closeness in a long term relationship. There are definitely people who don't agree with her approach, so up to you what you make of it. https://www.estherperel.com/?categories=Eroticism
Part of Esther Perel's approach is the idea of differentiation in relationships. From what you describe of how you strive to be a "good" husband understanding differentiation might be helpful for you:
https://www.instituteforrelationalintimacy.com/blog/differentiation-of-self-is-the-key-to-keeping-things-sexy-in-a-long-term-relationship
Hopefully some of these resources are useful for you, however, the fact that your wife won't communicate at all, won't even try getting mental health support for her own anxiety, and expects you to do all the work in many ways, not just sexually, is pretty concerning for the viability of the relationship. She sounds very shut down. I feel for you both. I have been in a sexless relationship myself, and it's very complex how these situations come about. In my case the relationship wasn't salvageable but therapy was very helpful for me (and was one of the reasons I trained as a therapist myself).
All the best to you.