I've not followed this as closely as I probably should, but hey it's the Internet so here goes
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For recalling knowledge the DM needs to be able to adjudicate whether the PC recalls the lore or not. For there to be a chance of success, the player should offer some approach to that recall, "I remember a lesson back in my "Lore you should know" class that covered strange shields and this one strikes a chord"... or "My uncle came from this region and often told regaled us with wild tales of its history"... It's really not a high bar (at my table at least), but it really enriches the time around the table, as players use these moments to enrich the backstory of the characters (or build upon an existing aspect of their backstory). It also acts as a minor gate to avoid just every PC rolling knowledge checks (so that eventually someone gets a super high roll and looks questioningly at the DM).
So just offer the DM something from your character's story (either made up at the moment, or pulling from the established backstory) that provides something adjudicatable (is that a word?!) ?
That's the agency bit for me. You,
the player, tells the DM how the PC possibly knows something about this thing.
the reason i try and avoid the player agency spins on discussions comes from the basic idea that "player agency" is a sort of stand-in for "the right way to play" (nobody is going to argue against "player agency" in the abstract) but its become so morphic that its definition can be applied to almost anything and even at times contradictory sides of the same situation. Recently saw it expanded to denying a Gm the right to alter/deny a PC fluff backstory element without being a jerk.
So instead i tend to not view "player agency" as more than a "the way i want it" kind of positive tag-on and instead focus on the actual effects and situations and mechanics being discussed.
In the cases you described i would have this to say
1 - it is not **always necessary** for a player to state that their character is attempting to recall a specific piece or type of information and also provide a backstory reference in order to resolve the question of "does my character know or recognize this thing or not" when such a thing is in question. The character knowledge is the character knowledge whether or not the player asks for it or not. Requiring these verbal hoop-jumps from the player before they can be given info their character has or be told they do not have is not giving that player more control or influence, it is holding back the in-world capabilities to the player's statements.
I think that is part of the key dispute going on here.
i certainly do not, and neither does [MENTION=57112]Gradine[/MENTION] i think but i will not speak for them, declare that a player *cannot* do just as you say - eclare their character is trying to recall a specific bit due to specific character reference. that can certainly occur at my table and my bet is at Gradine's.
But we do not insist thats *required* and also allow for cases where the character is given a chance reflected by an ability check to have that info without direct declaration.
Example:
Two character walk into a bar.
They see a strange carving of a snake headed figure on the wall.
it is described by the gm among other things in the scene.
both hail from nakadocias.
it is a carving of a minor demon from the lore of nacadocias.
it is reasonable to assume it might be recognized from folks of that region but not guaranteed.
i think gradine and i would suggest those character make int checks possible with lore or religion profociencies applying. if either made the check they recognized it - no action needed.
I think with gradine and i, if the player said when asked for a check "hey, you know, my background includes dad as a sort of demon hunter cleric type and that seems right up his alley." then we might give them advantage on the roll.
if the image was less demony/monstery and more of a scantily clad dancing woman of the same ilk - then maybe we would let it be a cursory description until the characters decided to take a closer look - investigate maybe.
these do not deny the player the ability to chime in with relevant background info.
A countrary position seems to be that these "call for checks" is somehow removing the players choices so instead the opportunity to recognize it is gated behind specific requests for specific actions and specific targets.
i feel that is even more "reducing" the player's and character's capability.
We are using skill checks to guide our description of what a character sees. this allows two characters to enter a scene and not have their character reduced to getting to see the exact same minimum amount of info that everyone else gets until the player declares an action to use a feature the character has.
Just like a character with a +10 perception gets more info on entering a scene than a guy with +5 perception, so the guy with +10 religion gets more info when walking into a room full of many types of priest than a character with a +5 religion.
its not all that different from how things work normally with description - the character with darkvision out to 120 may see more than the character with darkvision out to 60 and more than the guy with a torch and no darkvision at all. the 120' darkvision guy does not need to announce an action to use his darkvision to 120' range and what he is looking for, right?
So why should the guy with religion +10 not get a similar amount of "what you see" or "what you recognize" just as automatically, just as a matter of describing what your character sees - without needing a specific call for a action and specific call for a target of info to be recalled?
To myself and gradine (i believe) we see room for both ways of determining uncertain knowledge - a Gm call for check and a player call for check. its when it is reduced to only the one that we see a huge disconnect - especially if the reduction is described as favoring player agency.
