Well, I started electrolysis before i started HRT. I know, not what you are asking exactly.
HRT doesn't affect the thickness or amount of facial hair. As I had electrolysis and HRT, the facial hair did seem to grow more slowly. That might have been HRT, or it could be that the electrolysis operator simply was removing the faster growing mature anagen phase hairs, and the stuff that has been coining in is mostly immature early anagen phase hairs. (Hairs have a sort of 'life cycle' they repeat over time.)
I would not expect HRT to have a significant effect on an established beard or someone who has had facial hair for several years or more.
I'm at about the same place Liz is at, although I've only been doing electrolysis for 11 months. I've been doing more hours per week to clear and maintain than most folks are willing to do, and all but a little patch on my right cheek is cleared or 'old growth' now. What's showing up looks more like vellus hair at first and gradually thickens and speeds up growth over several weeks. Removal of this new growth (immature anagen phase hairs) is not as uncomfortable as zapping the old growth was.
I probably had Sasquatch and a bunch of spotted owls lurking in the old growth and fighting back...