The VA does it all themselves in-house. If a service is not available, then they send you to a Care-in-the-Community provider and that provider is paid via insurance. In the Midwest is Optum, out West there is Tri-Care. That happens behind the scenes. You don't have to do anything. My disability rating is only 10% service-connected, but all my medical care is covered. Yours would be too. The exception is medicines. I do pay a co-pay for meds, but top-shelf name-brand meds only cost me $33 for a 90-day supply. With the higher rating, your meds might be with no copay. You would have to ask. I don't know how that works.
All of the complaints that I have heard about the VA were from people who were in large cities. Here in Rapid City, SD (pop. 75,000) I have no complaints. Everyone here is top-notch professional and very helpful with my transition. I don't know if it will make a difference, but you could try going to a smaller town's VA clinic instead of Phoenix. Like Chandler, or someplace smaller. Since I am limited here and do not have many to choose from, I can't say it would make a difference.
I would definitely check into it. Get registered as a patient, if you are not already. Make an appointment to see a Primary Care Physician. Talk to them about what you want to do. They can send a consult to Mental Health for evaluation of Gender Dysphoria. Once that is done, your Primary can then either prescribe HRT or refer you to Endocrinology or Gynecology. They will write the prescriptions and monitor hormone levels. Your Primary can also do the consults for Facial Hair Removal or Voice Training if you are interested in those. They will know what services are available there.
Every VA Clinic is supposed to have an LGBTQ+ Care Coordinator on staff. Check the Phoenix VA website and it will tell you who that person is and their contact information. They can also help you navigate the care that is available.
This is a lot of information I'm throwing out, but I hope it helps you and any other vets who are just getting started through the VA.
Hugs!