I'm writing a story and I'd like to how trans people get/treat STDs. If they haven't had bottom surgery is it no different than someone with those parts who is cis? But if they have, what differences are there? How about someone with no genitals?
In general it's pretty much the same as it would be for cis people. Bloodwork and a urine sample are the standard, and aren't really any different based on what someone's genitalia is like.
Pap smears and other sorts of exams can be dysphoria inducing as well, and there's some situation where it may be difficult to use a speculum because of atrophy (which can be for all sorts of reasons, hormones, vaginismus, imperforate hymen, intersex stuff). And people whose vaginas are surgically constructed don't typically have a cervix, so pap smears don't really get done as far as I know. (Sometimes speculums are used for other things though, like making sure everything is healing right, trimming or removing stitches from surgery, etc.)
But for the most part, the differences for STI testing specifically are mostly social, and can go different ways based on who is administering the test. Pap smears are in particular stressful for trans people who may have genitalia that's been altered by hormones. (I know it's irrational but the worry about getting a boner during a pap test, for instance, has crossed my mind a lot.)
Some other testing can be thrown for a loop because of the way procedure etiquette works. I had to have a transvaginal ultrasound once to check for ovarian cysts and there were definitely parts of it that were weird for me. (Transvaginal ultrasounds involve the ultrasound wand going inside the front hole for an accurate reading of specific parts of the reproductive system.) For instance, the ultrasound tech was a cis man and as part of their protocol, a cis woman nurse had to be in the room while I underwent this procedure. I hadn't asked about that ahead of time or really thought anything about it - I was in the emergency room trying to get to the bottom of extreme abdominal pain and I figured I could endure what I needed to. But in an ideal world, I'd be able to ask for a non cis person to be in the room with me I think. (I came in an ambulance, which would not take my partner with me.) (It turned out to be a 4mm kidney stone by the way, no ovarian cysts.)
Another anecdote that may be relevant to this topic is that sometimes doctors get weird about not knowing what you're testing for, because they don't know what body parts you have (and which were added at what points, made of what material). Prior to the transvaginal ultrasound, a doctor asked me what "chromosomes" I had. I honestly told him I did not know, I hadn't ever had a karyotype test as far as I knew. The doctor stumbled over himself a lot and I don't remember what else he said right after that, other than he was fumbling, got corrected, and that he was clearly Trying His Best. I interrupted the second or third useless question with, "are you asking if I have ovaries in case it might be a burst ovarian cyst or something?"
He was instantly relieved and said yes, so I told him.
There's a big problem I've noticed, that when people talk about these sorts of topics, they aren't specific enough in order to address what they mean. We use euphemisms like "assigned female" because people don't know that someone "assigned female" can have literally any body type. People seem afraid to name body parts, so they use euphemisms that rely on stereotypes and assumptions in order to be understood. But when you realize that people "assigned female" can be intersex, can have hysterectomies, can have testes, can have phalloplasties, and that everyone's parts are more or less analogous (skenes gland = prostate, etc), you realize how useless these broad categories are. If you want to ask if someone could carry a pregnancy, ask if they could carry a pregnancy. Not if they have certain chromosomes or were DFAB. Specifics matter. If I knew I was XY, that doctor would probably have assumed that the pattern of people with XY chromosomes not menstruating would include me. And if I did have ovarian cysts, or even a pregnancy, this could have dramatically impacted my health outcomes. (There have been stillbirths because of situations like this where people did not act fast enough because of ignorance around trans bodies.) I could have given in and guessed my chromosomes when the doctor asked, but what if my answer turned out to not be true? And what if the lack of confidence in my answer saved my life in some way?
I realize this is pretty far deviated from your original topic, but in terms of testing difficulties, it does feel like the sort of anecdote that would be very informative about these issues.