Why are women far more likely to have long covid?

The leading hypothesis is the same one that explains why women get more autoimmune disease generally. Women mount stronger immune responses than men - protective in acute infection (men had worse acute COVID outcomes), but it comes at a cost: women are the large majority of lupus, MS, Hashimoto's and RA cases. If long covid is substantially autoimmune/inflammatory, as the autoantibody findings in the OP article suggest, the group already primed for autoimmunity is the one you'd expect to be hit hardest. Proposed drivers: immune-regulating genes on the X chromosome (e.g. TLR7) and estrogen being immunostimulatory where testosterone is suppressive.

Are they though?

  The results follow a 2024 study led by Dr Mulu Woldegiorgis that surveyed 11,000 people from Western Australia three months after they contracted COVID-19. Almost one-in-five (18.2 per cent) had developed long COVID. The researchers then monitored the same group of people six months after their initial infection.  

  “We wanted to get a sense of the trajectory for people with long COVID. After six months, the average number of symptoms remained stable, indicating little improvement,” she said. 

and from that study:

  In multivariable analyses, pre-existing health conditions at the time of initial SARS-CoV-2 infection and reporting fatigue, shortness of breath, and cough 3 months post-infection were independent predictors of persistent long COVID.

  Age, sex, and number of COVID vaccinations were not significantly associated with persistent long COVID. 

I've heard things hypothesized to be either differences in hormone levels, or the one that's more fascinating to me is it could be because an issue came up with suppressing the second X chromezone.

Or maybe it's documented more because they complain more?

Perhaps because it involves immune system dysregulation.