We're really good at detecting radiation. Like REALLY good. It's because we spent a lot of money during the Cold War trying to detect nuclear materials. This includes underground weapons testing, being able to detect underground nuclear signatures via satellites, and even very trace amounts on people's clothing because it can help detect spies. It then was found that these things could be used for tons of stuff, such as tracking not spies lol.

But seriously, we can detect levels thousands of times lower than what's dangerous. You can even get pretty good dosimiters for like $100 these days