They actually care a lot about illicit drug use because it's very relevant to your health. For instance, if you're on amphetamines and your doctor doesn't know it, anesthesia can kill you.
Whether or not THC affects thyroid hormones, weed use does not show up on a blood test for thyroid function.
I don't know where you live or the relevant laws, but you should have confidentiality with your doctors and you should not have to hide any drug use from them.
Be honest with your doctors. Worst case scenario you get a little patient education about stuff you already know like "Smoking is bad, regardless of what your smoking." Best case scenario, mostly for opiate or meth users, they know what medications would be contraindicated.
No it does not. They have an ordered thyroid panel and that’s it. They will not sneak in a drug screen against your consent. Besides, thyroid is a blood draw and drug screens are urine based. Blood drug screens are more expensive.