https://www.marketwatch.com/story/boeing-starliner-saga-do-n... claims "[There’s] no hazard pay, there’s no overtime, there’s no comp time". The top two threads on https://www.reddit.com/r/nasa/comments/1f0hi3o/how_do_astron... a) suggest a government pay scale with hazard pay for NASA astronauts, b) point out that they are likely paid as active duty Navy members instead.

On https://www.facebook.com/AstroClay/posts/do-astronauts-get-p... an astronaut (verified account of a NASA astronaut) mentions only a small per-diem.

https://space.stackexchange.com/questions/2264/do-astronauts... has a lengthy, but inconclusive discussion.

ChatGPT 4o-mini generates a vague "it depends" answer with no useful sources or statements that could be used to follow up with actual sources.

This is a question where I would have expected an authoritative answer to be easier to find. At least regarding your "like the military" statement, it seems like some astronauts are military, but what kind of extra pay they get seems to be hard to find.