That is an important question for GMs to ask, to avoid the following situation.
Player: I search the door for traps.
GM: As you touch it, contact poison seeps into your skin, make—
Player: Hang on, I never said I touched the door! That's not fair!
No, it's not.
It's not needed to avoid that situation it's not even a particularly good one due to its consequences.
It teaches the player "its what I say not what the character knows or is good at that drives the trap skill."
That tends to show used in play then lead to two tiers of skills. Ones driven by character traits and ones driven by player traits. Most classic example is social tasks where in some games the GM mostly treats it by what the player says, not character checks.
That tends to show in play thst a checklist of things to declare unless pressures prevent it is the safest most successful route. A "door procedure" gets put in place which makes sure to put "poke ar fir with dagger" and " use glass to listen" before " listen at four to avoid those ear bug things.
But let's look at your door and traps.
First, long long long before the first trapped door, the notion of how ability checks and attacks are resolved **and that failure can have setbacks" should have been made clear. Should have been shown and well established that this can lead to bad stuff.
So, character is competent at traps and player says they check.
GM assumes the competent trap seeker is not an idiot. Assumes that will include knowledge of some trap types. Assumes "checking for traps" includes things like "is their contact poison" not "well, yuck yuck, let's just grab it yup"
So the check is made, and if its successful, the poison was spotted and narrated as "you see some strange goo as you use your probe on the surface of the mechanism. Its definitely not just dust and grime. Possibly iocaine." Then you may describe a few options that the character would commonly know of for the player to consider.
What if it fails, well, since failure can be some success with setback and you have a skilled character, I go with "you begin searching but unfortunately, there was a poisonous residue early on that you checked for and missed did not get all of. I need you to make a blah blah save, at advantage because you did avoid a direct full on dose of it due to your skills and caution in checking, before we move on to the rest." Here, the players sees the benefits of having declared check for traps (chosen to apply that character trait) even with a failure in the advantaged save but still suffers a setback and the door has not been cleared.
Meanwhile a character who just went on thru the door not looking for traps gets a full dose and trap.
In between of course is the amateur untrained trap guy who can get any of these and more, depending on how much the GM decides the proficiency is or is not required. While many traps could reasonably require "thieves proficiency" to defeat or spot, I would not necessarily rule so for contact poison on a handle myself.
So, see, "how is your experienced character doing his job" was not knowledge the **player** needed to know for us to resolve it. The player side only required them to decide "this is a spot where applying my traps skill might help out and makes sense." Then it's the game mechanics and traits that resolves it.
Much like combat. Thry need to decide who to attack and what with, the when and where to apply their axe skill, but not how their character is getting around that armored hide and shield.
But that me, what works for us, not for everyone but to me the more you require player-side-know-howzstate-how for resolution of actions using character abilities the more problems you bring in - more than you solve.