In my (european) country overly drunk people[1] are locked up for the night in dedicated facilities, and let go the next morning. They also need to pay for it quite a lot of money (detention places are often jokingly called "the most expensive hotel in the city").

I'm not personally a fan of that, but it's quite common in post-soviet countries and very normalized (people are actually surprised when I tell them that not every country does that)

[1] Ultimately for their own good, not as a punitive measure. They are watched by medical personnel and don't risk dying of hypothermia. Still it's not something I'd like to experience.

No, drunk people who do stupid shit or have passed out in public are just locked up for night and then let go unless they injured or killed someone.