You still don't resolve the problem that if the player knows the result of his own fortune test, then the player has unreasonably high confidence in the presence or absence of threat - confidence that it is not clear the PC should share. If he "rolls a 20" or whatever indicates great success with the fortune mechanic, he can proceed with unreasonably high confidence knowing that there is a low change he missed something. Conversely, if he "rolls a 1", then the player can act as with great confidence that if something was present, he probably missed it and some sort of remedy should be applied (for example, now might be a time to use a charge from a wand or cast a spell). This contrasts with the a very natural interpretation of what ignorance - a very bad perception check - should actually mean, where the PC should have unreasonably high confidence in his perceptiveness.
We disagree.
When a character rolls to hit and gets a 2 and misses then rolls a 19 and gets a miss, do you accuse him of metagaming if he draws different conclusions from those attacks? If he decides after the 19 missed "better get advantage or switch things up" but didnt after the 2 missed, do you bring down the metagaming thunder?
In almost every task i have attempted and most challenging tests or tasks, i have left it with a good ferling, a goid sense of how i did.
Read that as "i saw the d20 roll".
On occasion i was wrong.
Read that as "i misread the DC".
The idea inserted by a GM that the d20 is an unfathomable mystery thing without any representstion of analog in gme is to me "the problem" - not that the player sees it.
There are a gazillion intangibles in a scene that we do not deep dive into that can cause it to be hard to or impossible to describe fully.
In my games that d20 roll is a representative of those intangibles that the character sees and we dont detail before hand.
Consider this...
A character swings his axe and rolls a 2. Do Many GMs narrate that as "for some totally unknowable reason your swing misses and you have to act in character like it hit or we are gonna have a metagaming problem"?
Nope?
Instead do actually quite a few GMs toss out say "your foot hit a slick spot on the floor and your swing went wide"?
In my experience, yes they do. (There are plenty of other narrative options and cases.)
But suddenly, when it comes to perception (and certain other checks) some GM leap on with gusto the idea of "the d20 has no in game reality analog for the character" and a player knowing that was a bad result w is a metagaming problem?
How about he rolls a 2 and gets "unfortunately a peal of thunder hit just as you were listening at the door so you heard nothing. Might do better after the thunder dies."
Or
"there is a lot of fragile tiles and degenerated stone and mortar so its not helping your first tests for secret doors. Now that you have seen that you can try other ways, might get better results."
Or
"The door opening stirred up a lot of dust, making it harder to spot things until it dies down."
In my experience most folks especially experts or folks with even,moderate experience dont walk away from a task with no clue how well it worked, how well they did - even when they dont know the outcome. They might be wrong in their guess (since they dont know the DC.)
That to me and in my game is what the d20 is and i try and narrate that for non-combat rolls same os for combat rolls.
But either way the "d20 equals objective confidence" is the norm in my game.
So, no metagaming problem.