I have no idea what this could be, but perhaps this may help you with regards to wondering if you're maybe forcing a voice without realising:
Singing!
Lol. You don't have to go do karaoke or anything but maybe just finding something fairly easy range, nothing too high and nothing too low, so no Beegees or Barry White

. But try and find something you don't know the words to but roughly know the tune. So that way you're concentrating on the lyrics (reading them) and less on how you sound or your voice. This is just a trick to kinda distract your brain. For example, when trying to help kids with balance I have them stand on one leg and juggle, so their brain is focused on the juggling and not on mentally trying to balance so that would be the same idea. Your brain would hopefully be too focused on getting the lyrics and tune right to worry, even subconsciously, about the voice.
Just sing along and maybe record that. Then talk into the mic a few hours before or after and compare the voices and range you're at and see what happens. If there's a noticeable difference that goes beyond just singing VS talking voice, maybe you're unknowingly straining your voice. Perhaps your subconscious feels your voice isn't right and is trying to make it so. Who knows?
If you're hoarse/sore though, don't be too ambitious with the singing - don't make it worse. If it hurts, stop!
I'm not sure how long you've been on T but I've noticed some hoarseness myself as of late and I keep being asked if I'm ill right now and I'm fine

.
Good luck with whatever it is though. Have you had blood work to check your levels are staying fairly consistent at a good range?
Hope it either starts to ebb or you find a solution!