Yeah, it depends on the doctor and what you need done. For the initial phase, when blood tests should be performed regularly and the dosage adjustments require a more expert touch, it's typical to use an endo.
But I'm going to switch to my own GP soon, as my dose has been stable for 2+ years post-op and I don't need any more dosage fiddling than the typical menopausal cis woman. (In theory I also don't need any more monitoring than the zero they get, as I'm on a similar dose, but he is happy to run all the required blood tests once a year at my physical just in case.)