We had "session zeros", and many players said they wanted "player agency" in the games. Of course, no one could tell me what that was other then the "internet buzz words". So I got a lot of "player agency is when the player feels fully responsible for their own actions (whether they were guided or not). As long as the player feels like their hand wasn't forced, they feel like their actions in a game are their own." Or "Player agency is whenever the player performs any input to make any (informed) gameplay decision." Or "Player agency is the ability of a player to affect the course of the game."
To be fair, it sounds like you wanted examples. If those are the definitions they gave you, I can't think of any D&D game I've seen that doesn't meet those definitions.
1. I'm not a fan of the players or characters. And the big part of this for me is I don't give out advice or help to the players ever. As the DM I answer factual questions, but not "Hey, is it a good idea for my 1st level halfling bard to dive into the Pool of Deadly Lava and look for treasure?'' I know a great many fan DMs would say "No, wiat, don't do that your character will die", I am NOT one of them. So..in the wacky way: because I don't tell the players what to do...they feel they lack Agency.
Aside from not being friends, I see no problem in this. But if I were to "read into this," I would say this might be an information problem as opposed to telling them what to do problem. You might describe something, and they want more specifics - to make an informed decision. And you might just give them the same information.
A small example might be a PC looking at a desk.
DM: In the corner of the room there is a small desk with no chair.
Player: I walk up to the desk and look underneath.
DM: It looks like a desk.
Player: Are there any papers on it?
DM: No.
Player: I touch the top. What does it feel like?
DM: It feels like wood.
Player: Are there drawers?
DM: Yes.
Player: (Who is now a little frustrated at having to gather basic information they should have known about at first glance.) I open the drawer.
DM: A series of darts flies out of the desk from various places. Give me a dex save.
I have seen DMs require players to ask for specifics. And I have seen players expect to be given specifics. In this case: small holes in the desk where the darts come from, drawers, material, etc. When these two meet, it sometimes causes consternation. And in my personal experience, many of those DMs say things like: "I just give them the facts," or "I give the players information. What they do with it is up to them."
The problem often arises when those facts or information is not thorough enough.
2.My game is loaded with lore and information. It's one of my favorite things. Even the player that just coasts through the game will have to go through a little. But then they would have to remember things and use things in gameplay. And plenty of casual players refuse to do this. They are "forced" to listen to flavor text, but they never speak to NPCs in character or interact much with the game world. Their character walks into an inn common room and sees an open book in the fire place that is not being consumed by the flames...and they just ignore it and say "when are we going to fight something?" This comes up a lot for the "informed agency" thing. Players say they "don't know stuff", so they can't make informed decisions. My counter is the players are unwilling to role play, interact or immerse themselves in the game to learn anything. And the classic "they don't write anything down"
Having great players is great. Note takers. Role players. Tacticians. Players that pay attention to detail.
But...
In my experience, DMs suggesting some piece of lore that players need to connect to, and then upset that they don't, almost inevitably fail at completing these things:
- Foreshadowing the lore.
- Give the lore a concrete connection to the players.
- Give the lore an isolated moment. Not placing it in with other descriptions or other pieces of lore.
- Highlighting the lore through NPC actions and/or PC-NPC interactions.
- Repeating the lore in several places.
- Give the lore a strong visual component.
Obviously, a DM can't do all these things for each piece of lore. But if you want them to notice something, the onus is on you as DM to make sure they notice, not the other way around. These are players that are sitting for hours and being bombarded with a lot of information. If you want one piece to stand out, then you need to make it stand out. Let's use your book in the fire example:
- DM: "The sign at the inn is strange. The wooden plaque shows a hearth, but instead of a stew pot cooking over it, there is a book. It appears to be roasting or something. You are unsure as the image makes little sense."
- DM: (To the lore bard of the group at a different time before the book encounter. Maybe when the lore bard was perusing a library?) "In the center of the library, you see a large memorial tapestry. It is a memorial to the brave people that saved the books during a fire. One part of the tapestry shows people collecting books from the burnt building after the fire. Strange that there were some books spared by the flames."
- DM: "You walk in. It is a common inn, like the dozens of others you've seen. One thing stands out - sitting in the fire in the corner of the room is a book. It is not burning. It is just sitting in the fire and looks as commonplace as a cast iron pot. None of the patrons are even looking at this book sitting in the fire."
- DM: (During the group's meal) "The bartender delivers your meal; porridge full of carrots and potatoes and a little meat. Directly after, she walks over. Her long gait and thick shoulders look like she's in a hurry. Amazingly, you see her grab the fire poker, and start to turn the pages in the book, like she is spreading out coals."
- DM: (Looks at the players and one of them asks for a history or arcana check to see if they know anything about this book.) Based on the roll, the DM gives a history of this book which was once a gift from an elemental wizard to a fire giant. How it came to this inn, you have no idea. The DM also states there were dozens of these bequeathed to the fire giant kings by that same wizard. They were built so the fire giants could learn to read.
- DM: (One of the players says their character is going to have a closer look.) "The fire licks at the book edges like a tongue testing to see if a piece of food is too hot. The blue coals near the base illuminate the thick leather coating, which should be aflame. And on top, at the pages it is open to, you see a Dwarvish script in what you think is the language of the giants. The handwriting is neat and level with little flair. On the other page, you see a small charcoal sketch. It looks like a cartoon; a dwarf and giant sitting together, and the dwarf is trying to dive into the giant's mug of ale."
Obviously, this takes a lot of prep. And if these players want that, and you're an impromptu type of DM, maybe that is part of the problem. And even for a prep DM, the players might ignore this. That's okay. That's why you should prep other stuff too. But sometimes DMs throw things like this, and a dozen other things out there. When there are too many, it becomes mundane. If you want something to stand out - you as DM, need to make it stand out. It's a balancing act between railroading, choices, player agency, and session zero expectations.