Hello Synthia,
Like Cassie, I too wear contacts, and suffer from dry eyes from time to time.  When I went to the optometrist for a consult and to get fitted for contacts, he specifically asked me what medications I was taking.  When I told him that I was TS, and the HRT I was prescribed he warned that there could be side effects that would affect my eyes while wearing contacts.
It seems that both you and Cassie suffer a lot more from dry eyes than I do as I've often forgotten to take my soft contacts out over night without suffering.
I've seen the literature on RGP lenses, but my optometrist advised against them for me as I wear bi-focal contacts..
Here is an article on them:
http😕/www.allaboutvision.com/contacts/rgps.htm
As for those foggy moments... oh yes, but I don't think it's because of HRT.  You should not be getting that type of side effects from HRT, but then each of us is different.  I would recommend you contact you Dr If it is becoming a cause for concern .
Chat later,
Steph