Ovinomancer
No flips for you!
I think this needs unpacking, and I'll do it without defining anything.I'm sorry, but it is you who is trying to separate the game and roleplaying. It is a roleplaying game, all of it is part of the game, even when no formal rules are involved. It can have no rules beyond 'players decide what characters do, GM decides what happens and describes the world' and it is still a game, a LARP is a game.
Also that 'the characters talk and decide to do something' is crucial for agency. That is them establishing the direction of the game, you can't get more important act for agency than that.
Firstly, the claim that players talking and deciding things in character being crucial to agency is immediately defeated by examples of agency being wielded even while in pawn stance -- ie, without any attempt to portray the character. This isn't terrible interesting to your point though, so let's set this aside and look at cases where players are talking and deciding things in character.
In this case, the discussion between players doesn't really get to agency until they act on that decision -- if you've ever attended a meeting where courses of action are being presented then you'll recognize that what's said in the meeting has only a loose connection to what actually happens (except in rare, special cases). Just agreeing between players doesn't make a thing so -- it's the actions taken to enact it that really get to agency. And, here, we're back to the same evaluations -- who's doing the resolving? If it's just the GM, then no amount of discussing or deciding in character will overcome a GM veto. There's no agency here at all. On the other hand, if the GM authorizes the plan, then we can evaluate agency. Or on the gripping hand, if the system allows players to push the issue without the GM's authorization, then we can also evaluate agency. The details of what's discussed and decided don't matter until put to action, at which point the agency of the game will show up. Just talking in character doesn't enable or disable agency.
Now, is it important for other reasons? Absolutely! I'd find my RPGs to be rather dull affairs (I'm not a fan of classic player-skill dungeon crawls) without some good characterization! And I think that making choices that advocate for your character is very important for my enjoyment. But, doing so doesn't enable agency, so I can't agree that in-character play is critical to agency. It's critical to my enjoyment, though.
I'm not sure what you're criticizing, here -- it's not anything I'm familiar with. I 100% agree that the Lancelot character's player doesn't control outside characters, and that the conflict is key to the play, but I don't know what system you're talking about that would offload this to some mechanic and rob the player of agency.Something is at stake! And that still needs no rules for happen. It is the narrative that creates the stakes, not the rules.
Now for back to our friend Lancelot. 'I'm love with the queen' is an important driving force for the character, it is part of his central motivations. This sort of character defining driving force is something the player should accept, otherwise the GM, system or whatever, is effectively creating the character for the player (and if players agree to that, then its fine, but they're willingly giving away a part of their agency.) But being able to decide 'this is what my character cares about' is pretty damn central for agency as it is from those core beliefs all the other decisions follow. Lancelot is in love with his best friends wife, and the fate of the nation depends on this friend. But the player does not control Arthur, they do not control Guinevere, they do not control the other NPCs (unless this is the sort of game where player has narrative level powers.) Numerous risks and conflicts arise from this central motivation, and it is for the player to decide how to handle these situations, what choices to make. Relegating these vital choices to some mechanic would rob the player from agency, make them a spectator and is bizarre to think otherwise.
For example, if the player of the Lancelot character find a situation where they can act on their forbidden love for the Queen, but it's in tension with their loyalty to their friend, does the player have agency by just saying they resist and their character resists? This is a Czege violation -- the player has established both the forbidden love and the loyalty aspects and then also establishes the resolution of the tension between them. This isn't playing a game, or engaging agency, it's just straight authorship. It's isn't low or high agency because agency isn't invoked.
Now, you can also have the GM decides aspect here, and the GM can decide how the character reacts. This is clearly a low agency situation -- the player can only try to persuade the GM to issue a preferred resolution, but has no ability to influence it otherwise. This gets a bit better if the GM decides a check is in order and the player can then leverage character abilities to improve the odds of success, but, again, what success and failure is will be decided by the GM. The best that can be hoped for here is a keenly interested GM that will act as benevolent dictator and deliver a fair evaluation/resolution and that you like this. I find most D&D games live in this space -- the players like how the GM decides things. Or, don't dislike it.
Alternatively, you can have a situation where the GM can say, "sure, you resist," or they could say, "um, this seems like a good time to see which side of Lancelot wins, let's have a check." The terms of this are system restricted -- on a success the player gets what they want, on a failure the GM can narrate the failure state. Note this differs from the above in that the ability to dictate resolution steps is shared -- the player gets to dictate the success, the GM the failures. The player here has more agency because they can set at least half of the wagered outcomes and the GM cannot gainsay them.
Finally, in an interesting case, the player themselves can ask for a check because they're interested in both a situation where Lancelot resists and one where he doesn't. This can go to all of the above situations -- player decides all ends of the wager, in which case agency isn't invoked and the check is just an aid to deciding how to author the scene; or, the GM decides, and agency is reduced in favor of elevating GM agency; or the system has a say in how the check will be conducted and the player has more agency by dint of determining some of the resolution space without GM approval.
None of this looks like turning over the character to mechanics. In any case where agency is invoked (and just dictating outcomes doesn't invoke agency -- it's not no agency, it's not even agency) there's always a mechanic involved, even if that's just GM decides.