Apple Watch on its own will only detect sleep if you sleep with the Sleep Focus enabled. You can schedule Sleep Focus to auto turn on at your scheduled sleep hours.
There is an app called Auto Sleep which is a cheap one time purchase app. A lot of people love it for its ability to auto detect sleep. Personally, I find the UI within the app to be atrocious and very difficult to read. Also, the sleep stages “deep sleep, light sleep” etc., will NOT be visible within the health app unless you had Sleep focus enabled. If you sleep with Sleep focus disabled, the auto sleep will pull your time slept into the Health app.
Sleep stages will be visible within the auto sleep app itself, however like I said, the UI IMO is terrible.
Here’s a screenshot of my sleep data in the Apple Health app. You can see the parts where auto sleep pulled data into Health (and I had sleep focus disabled) because those datapoints do not have sleep stage information.