Mine take a sample of my blood and use their own on-site lab to measure the levels of about twenty enzymes, hormones, glycoproteins, blood cell counts and whatever. A few days later they send me a report with the levels, and they adjust my medication if necessary.
They talk with me about my experiences, my emotions, whether I have observed breast growth, whether I sleep well, how I feel about my transition and so on.
I ask whether changes in my medication are possible, like using a different combination of estradiol gel and tablets, and whether we can add bioidentical progesterone or some testosterone for my libido or an estrogen cream after my SRS.
They give me a prescription for my medication lasting until my next visit (first every 6 weeks, then every three months, now twice a year).
They have never done any examination of my breasts or testicles, and I do not think it would be their job. They did however advise early in my HRT that I should have my breasts checked regularly.
I should probably add that they have many trans patients and they seem to know their (and my) business.