Passive Perception doesn't "just happen."
Passive Perception is a special kind of ability check that occurs when the DM must decide, for example, if a character is surprised by a monster or notices a trap or hazard while traveling. You cannot have an ability check without a corresponding task that carries with it an uncertain outcome and a meaningful consequence for failure. This is covered in the rules for ability checks in general and passive checks specifically.
While it's common practice in my experience that it is assumed that a character is alert to hidden dangers unless otherwise stated, that assumption still means that the character is actively on the lookout for danger. There is nothing "passive" about the task the character is undertaking, repeatedly. "Passive" just means there's no die roll.
A DM is well-served in my view to avoid making too many assumptions about what the characters are doing or telling a player how his or her characters thinks or feels about things. That's the players' role. The game works best in my view when everyone sticks to the roles the rules of the game prescribe.
A Passive Perception check can be something like repeatedly searching for something, but I think it can also be actually passive, thus the name.
Darkron Is in his home and walks into a room. An assassin stands behind the door hiding. Darkron isn’t actively searching, but as a DM I’ll use his passive perception score to give whoever it was that came through the door an opportunity to notice the assassin or something strange just because their senses are so acute.
I think it is the DM’s role to describe what a PC experiences — sometimes that might involve telling players what they feel and thoughts that might occur to them. Then the players’ role would be to respond to that stimuli. I’m not at all saying this should be done often or maliciously or to railroad. A DM should learn how they group works best and employ a tool like this if it benefits the group.
The basic tenets of the game are:
1. DM describes.
2. Players act.
3. DM narrates results.
To me, a feeling is not something I do. Thoughts that pop into my head are not something I have conscious control over.
What I do is react to my feelings or random thoughts.
I don’t choose to feel sad, but I can try to do things to snap out of it.
I choose to eat a sandwich that has spoiled and then feel like I want to die, but I certainly don’t choose to feel that way; that is a result of my action. I can then act to relieve that feeling somehow.
My feelings are can result directly from my actions, but sometimes they result in how external stimuli affect me whether I want that to happen or not.
As a DM, I might ask the spoiled sandwich eater to make a Constitution saving throw. Pass or fail, I’d describe how they felt: “you feel your Stomach grumbling a bit” or “your stomach is tied in knots and may soon explode.” I wouldn’t leave the choice if feeling to the player.