Clots are probably the number one short term risk when using AAS or even TRT. Even if something else ultimately causes the clot, it is likely that any AAS use is a contributing factor. Even if using AAS does not cause a clot, it makes it easier for other things to cause clots.
It is VERY common for doctors to throw you on some blood thinners and never actually treat the conditions that caused the clot to form in the first place. This is especially true when the clots arise from surgery or trauma.
It isn't enough to just take an aspirin a day and call it good, you need to monitor your blood work carefully and take appropriate steps as necessary. Ideally you should have a doctor who is aware you are on AAS or TRT and is monitoring your bloodwork.
Even if you are normally fine with thick, sticky blood, all it takes is an accident or surgery and you could throw a clot. Plus your heart is working harder all the time to pump overly thick blood.
There is a surprising number of people who can be a walking time bomb even on very low doses or just TRT, while others can have no issues at all even on larger doses. This isn't something you want to gamble on, and you don't have to with simple blood work.