Wow, this semms really really bad. So someone can step into the bushes and "hide", then walk in broad daylight with zero cover from anything and stroll past 100 people undetected. They can't even notice the rogue, because you need to choose to make a perception action to attempt to detect them? Why would you randomly make a perception check to look for something invisible?
What a design fail
So, after some discussion and analysis, I don’t think that’s actually RAI. There
is a sidebar about passive perception, so it does seem to still be a thing, so if a creature’s passive perception is higher than the rogue’s stealth check, it
should still find the rogue. Additionally, there seems to be some ambiguity about if the “invisible” condition actually makes you invisible. Two of its benefits specifically don’t apply to creatures that “can somehow see you,” and I think it’s safe to say that if a rogue is not actually under the effects of the invisibility or greater invisibility spell, a potion of invisibility, or a magic item that turns them invisible, then any creature with line of sight to them should be interpreted as being able to “somehow see” the rogue, even if that makes the condition stupidly named.
The interpretation I will be going with until/unless new information is revealed that changes my mind is this:
To hide, a character needs 3/4 or full cover or heavy obscuration, and then must succeed on a Dexterity (Stealth) check against the higher of 15 or the highest passive perception among hostile creatures in the vicinity. On a success, the character gains a condition that grants them advantage on initiative rolls, advantage on attack rolls against creatures that can’t see them, and imposes disadvantage on attack rolls against them made by creatures that can’t see them. This condition ends if the hidden character makes a sound louder than a whisper, makes an attack roll, or casts a spell with a verbal component, if they enter the vicinity of a hostile creature with a higher passive perception than their stealth roll, or if a creature uses the search action and beats their stealth roll with a Wisdom (Perception) check.
If we just ignore that the condition is called “invisible,” all of this is mostly reasonable. I don’t really like the DC 15 floor for the stealth check, or the fact that any creature detecting the rogue “breaks” their stealth for all other creatures. But other than that I think it’s actually fine.