It is the DM’s job to interpret the rules and apply them using their best judgment. If the DM rules that an action should be resolved by way of a Dex save, then a Dex save is the way by which it shall be resolved. But, if you don’t like that example, imagine I said they called for a Dex (Athletics) check when you wanted to make a Dex (Acrobatics) check because you’re proficient in acrobatics but not in athletics. Point is, the player doesn’t get to decide what mechanics are applied to resolve their own actions. And yes, sometimes that will mean some of your character’s features won’t be applicable to some actions.
Deciding which proficiency applies is fair. But, again, you have decided that it must be a passive and that it cannot possibly be active. This bothers me, but you keep saying it shouldn't bother just because the DM can make up whatever justification they want. That's not a good argument in my mind.
But they can’t know there’s nothing in the room if they don’t search it. They can make a reasonable educated guess based on the description of the environment and the presence or absence of telegraphs therein, and decide based on that educated guess whether or not it’s worth their time to search. That’s a decision that’s up to the players to make, not me.
Let's say that they make the decision to search then. Why not just say "You don't find anything of note" and move the clock hands forward? If you want to give them a consequence for choosing to search a room with nothing in it, you totally can without having them actually search anything.
So, why do you not do that and instead have them search the room manually when you know there is nothing noteworthy in it.
sigh I keep telling you, I do have lots of knowledge of what’s going on. What I don’t have knowledge of is what among “what’s going on” will end up being important and what won’t. To answer your question, yes, if there’s something hidden in the room, I will know it’s there.
Why do you not know? If there is nothing going on involving Shar, then an idol to Shar wouldn't have any importance to what is going on, correct?
As do PCs, when the person hiding fails to beat the PCs’ passive Wisdom (Perception) with their Dexterity (Stealth) check.
And I have done so when taking an action that I do not take repeatedly. Which isn't a passive check.
Yes, you are wrong about it. I set up the initial conditions, and the players do what they will from there. I can’t know if any given thing in the environment is important, because I don’t know what the players will do with it, or even if they will ever see it. Like, imagine a room hidden behind a secret door, with like a dragon-slaying arrow in it. Maybe the players will find the room and take the arrow, and maybe later they’ll encounter a dragon and use the arrow to slay it. In that case, the arrow ended up being pretty important. But when I designed the dungeon and placed a hidden room with a dragon slaying arrow in it, I didn’t know if the players would find the room, I didn’t know if they would take the arrow, and I didn’t know if they would end up encountering a dragon later. It could have ended up being entirely unimportant. We have to play to find out.
Wait. The only way that arrow would be important is if they end up encountering a dragon later and they use it? That has NOTHING to do with what I'm talking about.
I'm talking about things like the Dragon-Slaying arrow being in the secret room because it is a clue that the Duke was once secretly an adventurer, a secret he is hiding. It is important because it informs something else and gives them context or reveals things about the location or an ongoing plotline. It sounds like you are using "important" to mean something like "I didn't know that pipe was going to be important until they used it to bar the door". It wasn't important when they found it. They found something unimportant and utilized it (which is why my inventory is always full of miscellanous stuff) I'm talking important as in it tells the PCs something they didn't know before, or confirms something they suspected.
If you just have random treasure that may or may not be worthless, that's not actually important.
I don’t know if there will be a roll to which the the bardic inspiration could be applied.
But you heard them make the plan. The plan that you knew you would regulate to a passive check and would not be a roll. Would you not tell them that?
No, not when they move to the center of the room. When they declare an action (with clear goal and approach) that could succeed at finding the trap, could fail to find the trap, and has consequences for failure.
They declared an action, with a clear goal and approach. That action was to search for traps by moving to the center of the room. They could succeed in finding the trap. They could fail to the find the trap. And it has consequences for failing to find the trap.
Since the trap happens to be in the center of the room, do they get to roll to find the trap?
Different action than what? You didn’t describe any action in the example.
Yes I did. Moving to the center of the room to look for traps. That is an action, you clearly can picture it, it gives positioning. It has every single factor you have asked for. Do they get to roll to find the trap?
Then we have different definitions of reasonable specificity.
Clearly. If someone told me they were going to search a room, I'd know what they are doing and where they were. Seems reasonably specific to me.
I can imagine searching a room as a thing someone could do, but there are so many possible ways a person could go about doing so, I cannot form a clear mental picture of how a player’s character is doing so, unless they narrow it down for me or I make assumptions, and I do not want to make assumptions about the what the player wants their own character to do.
No, because it’s still too vague what they are doing in their search of the room. It leaves the fictional action an abstract haze, which doesn’t work very well for forming a consistent shared fiction.
Why does it matter EXACTLY how they are searching the room? There are many ways I could go about running too, multiple techniques and styles, each with pros and cons. But I don't need to ask someone HOW they are running. They are running, that is good enough.
That’s a way one might choose to resolve such an action, sure. For me, it’s too abstract. Can’t form a clear mental picture of what actually happened to result in the trap being sprung or not.
And here it is again. What matters is "did they declare an action which springs my trap".
It isn't about not understanding or not knowing, it is that you want them to state exactly what they are doing, so there is no question if they triggered the trap. Even if their action is to specifically look for traps so they don't spring them, you need to know if they randomly guessed the wrong thing to say, so that they actually sprung the trap before they get the chance to look.
And if this isn't the case? Then you could just remind them that failing the roll could result in any hazards in the room being activated. If they agree, then they also can't complain to you about the fact that they triggered the trap. Simple fix.
Why can’t they? They can make up whatever they want.
Because unless you state "This is from Tyr" to a group of people who aren't from Tyr, no one knows to make up the fact that they are from Tyr.
You seem awfully concerned about the possibility of failure without a roll, to the point that you would rather risk a swingy d20 roll than try to pursue success without a roll. That seems absolutely bonkers to me, but it is certainly your prerogative.
Because "you fail without even getting a chance to try" sucks. I'd rather have some chance of success than zero chance of success.
See, that sounds awesome to me. We’re gradually learning more about the character through play. That’s emergent storytelling right there, which to me is what D&D is all about.
I don’t agree that it boils down to the same thing at all. Like, I guess, in a strictly mechanical sense they might be resolved similarly. But in the former case you’ve generated and established a cool story about this character and their relationships with the people they met while studying magic, while in the latter case you have nothing but a vague abstract haze.

Sorry you feel that way I guess.
I can get the same backstory of people and relationships in magic school without them needing to make up a new fact every time they encounter something magical in the world. And it will be far more coherent and far easier to work into the story naturally than something they made up on the spot so they didn't need to risk rolling when they encountered swamp magic for the first time.