I honestly think that one of the sections of the DMG in Running the Game should have been about how to handle hiding and stealth.
As with many others here, I have my own set of rules for how it works. I think that - presently - the gold standard for comprehensive stealth rules goes to Pathfinder 2. I can also see why D&D doesn't want to go that route. They're hard to wade through except for Rules Nuts like me.
One of the things that is really confusing me is how passive Perception ties into this. Because, as you might be already aware, passive Perception has been massively downgraded in the new rules. It doesn't get a mention in Chapter 1, and a minor mention in Chapter 2 (Creating the Game).
But then you get this text in the DMG (Chapter 2 - Running the Game):
When to Call for a Check
An important time to call for a Wisdom (
Perception) check is when another creature is using the
Stealth skill to hide. Noticing a hidden creature is never trivially easy or automatically impossible, so characters can always try Wisdom (
Perception) checks to do so.
Using Passive Perception. Sometimes, asking players to make Wisdom (
Perception) checks for their characters tips them off that there’s something they should be searching for, giving them a clue you’d rather they didn’t have. In those circumstances, use characters’
Passive Perception scores instead.
Read the first paragraph. So, is the DM
calling for the players to roll, or are the players
choosing to roll? It seems both.
Then the second paragraph. If there's a creature hiding in the room, the DM starts using passive Perception... which indicates that, all of sudden, that becomes relevant for Stealth again.
Sidenote: Passive Perception is mostly unmentioned in the PHB. Except in the spell effects for
Enthrall! Chapter 2 has how to calculate it and write it on your character sheet. The Rules Glossary does have it as a topic (hooray!)
Chapter 2 (Fill in Numbers):
Passive Perception. Sometimes your DM will determine whether your character notices something without asking you to make a Wisdom (
Perception) check; the DM uses your Passive Perception instead. Passive Perception is a score that reflects a general awareness of your surroundings when you’re not actively looking for something.
Rules Glossary
Passive Perception is a score that reflects a creature’s general awareness of its surroundings. The DM uses this score when determining whether a creature notices something without consciously making a Wisdom (
Perception) check.