But the DM doesn't get to rule when Dex saves happen. The Game Rules say that. If the DM suddenly said "The orc swings his axe, make a dexterity saving throw!" I'd be more than a little confused, because the rules for an attack say that the orc should be targeting my AC.
Honestly, I've never heard of any situation where a player's action was resolved with a dex save, because dex saves represent dodging and you can't take an action that allows you to dodge an attack via a Dex Save. So, I don't see the correlation at all. And if a DM said "Okay, make a dexterity saving throw to swing on the chandelier" I very much would say, "Um... do you mean an Acrobatics check? Because Dex Saves don't work that way" and if the DM insisted that they get to decide how to resolve actions, so they decided it was a dex save, I would in fact be more than a little miffed at them.
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.
Okay, so previously you said you have no idea if there is anything notable or important in the room. You zeroed in on clues thinking I was stating you set up a mystery. Now you are flipping back, the players are going to search because they don't know.
So, back to the question I asked. If there is nothing noteworthy in the room, why aren't you telling your players there is nothing noteworthy, instead of having them waste their time searching? Especially since you have a time pressure and if they knew there was nothing in here, they wouldn't bother.
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.
Second question. If there is something noteworthy in the room, then you should know it exists, correct? So why is it you can't know what they may want to find, since you know what is worth finding in the room? And if you are about to type "I don't know" then why do you not know? Because frankly, I do not understand this style of gaming where the DM has no knowledge of anything going on.
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.
And yet, I have found people by looking around the room, noticing what has been changed or moved, or seeing a shadow move, without having to start moving anything.
As do PCs, when the person hiding fails to beat the PCs’ passive Wisdom (Perception) with their Dexterity (Stealth) check.
How can you not know what is important? To me, it is sounding like the players are telling you what is going in the scene, not the other way around. Can you explain this because all I can imagine is the players looking at an item they found off a random chart, explaining the story they just made up about why that item is important, and then you writing it down and making that the truth of the situation. But I have to be wrong about that, right?
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.
Would you tell the bard not to bother giving the fighter inspiration for the roll, since there would be no roll?
I don’t know if there will be a roll to which the the bardic inspiration could be applied.
Not every monster-infested dungeon or treacherous wilderness tries to kill you every 10 minutes on the dot, to force you to continue moving from the safe zone you just created.
I’m not sure what safe zone you’re talking about, but regardless, 10 minute dungeon turns don’t have to mean the dungeon tries to kill the PCs every 10 minutes. There are lots of dials you can adjust - how many turns pass between rolls for complications? How likely is a complication to occur when such a roll is made? How deadly are the complications? Adjusting these parameters is a great way to create dynamic difficulty; maybe the Dungeon of Terrible Deadliness has more frequent, more likely, and more deadly complications than the Cave of Mostly Just Bats. Either way, the time pressure still encourages the players to weigh their priorities and be economical with their decisions. Mayne that doesn’t sound like fun gameplay to you, and that’s fair enough, but it’s a lot of fun for me and the people I play with.
Okay, this directly contradicts what you said before. If when they declare they are moving to the center of the room to look for traps, you allow them to roll a wisdom check to try and find the trap in the center of the room before triggering it, then there is no issue. Previously, you said that it would trigger.
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.
Now, if instead you are saying that they had the chance to take a DIFFERENT action that would have given them the chance to find the trap, but moving to the center of the room triggers it regardless, then you are ignoring my point.
Different action than what? You didn’t describe any action in the example.
See, this makes me think that with the above, you really were saying that they could take a different action.
Searching a single room is more complex than searching a single container, but it is still reasonably specific.
Then we have different definitions of reasonable specificity.
I can easily picture someone searching an entire room. In fact, I bet I could send you multiple videos of it happening, it is rather trivial.
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.
But, that isn't the uncertainty you have. The uncertainty you have is whether or not the trap was activated before they find it. So, if there were no traps in the room, is searching the entire room a reasonable action? You don't need to worry about whether or not they trigger the trap after all.
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.
And, since there is uncertainty in the outcome of the action... doesn't this just mean the dice get rolled? If they roll low, they stepped on the trap first, if they rolled high they found the trap first. That seems perfectly within how the rules of the game are supposed to work. If you are worried about the player complaining, then all you have to do is say "I'll let you roll, but if you roll low you will be exposed to any hazards in the room, as a consequence of not spotting them before dealing with them." And if the player still agrees to roll, then they can't turn around and complain, because you told them that would happen.
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.
They don't have to guess AS LONG AS YOU REMEMBERED to tell them the symbol is from their backstory.
And if they are making it up, they can't make it up based on it being from Tyr, unless they know it is from Tyr.
Why can’t they? They can make up whatever they want.
And this I think gets back to the point.
If a player says "I think back to my Arcane Studies" they will likely get a roll. But if they say "I think back to my Arcane Studies in Tyr" they may auto-succeed... but then they may fail other checks, because being from Tyr there are things they would never see. So the best move would be to be as vague as possible, because that allows you to roll, while never locking you out of succeeding.
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.
Or, you get the other method, where they say "I think back to my Arcane Studies in Tyr" then later say "While in Tyr, there was an adjunct professor from Evermeet" and then even later "While in Tyr, while in the class with the adjunct professor from Evermeet, I met a student who had come from Silverymoon." Followed by "While in Tyr, while in the class with the adjunct professor from Evermeet, with the student who had come from Silverymoon, we had a rival who specialized in Diabolic studies."
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.
And at the end of the day, you have this convoluted set of circumstances that basically boils down to the same general thing the other player said "I think back to my Arcane Studies".
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.
Frankly? I got annoyed with players who constantly made up new random things, because they did so seeking advantage on the check, and it was also specific to this situation, but still general enough that they could make up something new for the next situation. I don't ban people from making up those details, but we mostly do it after the roll if we need to, or just go with the backstory they created before we started.

Sorry you feel that way I guess.