I was wondering how being invisible without being 'hidden' (because you didn't use an action to Hide) interacts with Perception/Stealth.
I'll speak to how I run it.
If you're invisible but not hidden, creatures that are close to you can pinpoint where you are. They can attack you (albeit with disadvantage). If you're hidden, they don't even know where you are and can attack a place, hoping you're there. In this case, they have disadvantage, but even if they roll a 20, they have to be targeting the right spot or they miss.