Disease control is one of the primary tasks of customs and immigrations agencies around the world. This authority was exercised quite prominently in 2020. But it is also exercised pretty mundanely on daily basis in regards to the transport of agriculture that carries diseases of agricultural concern... much to the frustration of travelers with foreign snacks.

From the US Government USCIS Form I-693 Instructions:

The civil surgeon is required to perform specific tests for tuberculosis, syphilis, and gonorrhea. The medical examination also requires the civil surgeon to evaluate for other sexually transmitted diseases and Hansen’s disease (leprosy).

Furthermore it suggests that physical and mental disorders may be grounds for disqualification. Finally, drug addiction and substance abuse generally must be disclosed.

https://www.uscis.gov/sites/default/files/document/forms/i-6...

Many countries do this for immigration. In New Zealand they say your test result doesn't affect your application. Whether that's true I don't know.