Typically, GMs put down objects, potentially important ones, in a location for PCs to interact with in some manner, such as to take, destroy, or use. Spellbooks are usually considered important objects--although apparently not in BW.
This is not how BW works. At the core of BW is the framing of the scene - establishing a situation that, in some manner, engages or challenges or puts pressure on a PCs' Beliefs, Instincts, Relationships etc - and then the resolution of action declarations. (Which is via "intent and task", "say 'yes' or roll the dice", and "let it ride" - you can read more about all these in the free PDF that I pointed you to not far upthread).
Hidden notes, that the GM gradually reveals by using them as guides to action resolution as players "poke" at the setting, are not a very important part of play.
That's not to say that the GM mightn't have secret ideas. But these don't serve as guides to action resolution as players "poke" at the setting (cf the way a map and key works in typical D&D play, which precisely does have the purpose of guiding action resolution when players declare actions like "We search for secret doors" or "We listen at the door"). Those secret ideas might provide material to draw on in framing, or in narrating consequences. They are like aides memoire to the imagination; they are NOT pre-established elements of the shared fiction, just waiting to be shared by the GM in the manner of a D&D map-and-key.
Another thing about BW (and any play that allows the players to set the stakes) - whether or not an object is important is something the players decide, not the PCs. I mentioned upthread that Aedhros, after not killing the innkeeper due to Alicia's Persuasion, nevertheless stole his shoes so that he (Aedhros) would not have to go about barefoot. (Aedhros had no shoes because, in PC build, I couldn't afford them, give the other things I spent my resource points on.)
In D&D it would be unusual for ordinary
shoes to be a significant focus of concern in play. But for Aedhros, with his Etharcal trait (so he knows what it is to live as Elven nobility) and his Instinct to repay hurt with hurt (and the innkeeper had hurt him, having swindled him and Alicia and tricking her into working in the kitchens), getting back at the innkeeper by killing him and stealing his shoes and his cashbox was an intense priority.
can a GM in Burning Wheel decide to place a spellbook (or any other object) that is designed to be interacted with by the PCs without the PCs have to declare that they want to use such an object? I'm guessing no, because you described my MotW idea as not being what you would like to play--which strongly suggests that this game is incompatible with mysteries, horror, twists, unknown assailants, or unforeseen circumstances, which is the type of game I like playing and running.
On horror, twists etc I refer you to the other thread where we discussed these things in the context of AW play; and also to my example of Thurgon discovering letters that reveal him to be the grandson of a demon summoning wizard, which involves a twist that is rather horrible. Alicia being swindled to work in the kitchens is an unforeseen circumstances. Etc. Burning Wheel (and AW, and I would suggest DW too) have no trouble with any of this.
But when you ask can the GM "decide to place a spellbook", what do you mean? I can place a real cup on a real saucer, but I can't literally place an imaginary cup on a real saucer, and of course if I imagine placing an imaginary cup on something well I'm not
really placing anything on anthing.
If you mean,
can the GM make notes about what things might be where, sure, why not? If you mean, does the GM refer to such notes as a step in action resolution, interposing between "intent and task" and "say 'yes' or roll the dice" a step along the lines of
say no if your notes dictate it can't succeed then the answer is no. And if you mean, does the GM refer to such notes as a step in action resolution, as a reason to say 'yes' independently of what is at stake given the player-evinced concerns for their PC, and their intent in declaring the action, then the answer is also no.
This is an example, not really an explanation as to why things happen.
To be honest, I feel I've been pretty painstaking in my explanation of the processes of play. But you keep building in assumptions that I have not asserted and have repeatedly said are not part of those processes - eg you appear to keep assuming that the GM will have regard to a map, notes etc in resolving action declarations in ways that are independent of "intent and task", "say 'yes' or roll the dice" and "let it ride". See, eg, this post of yours:
In a case like this... because it's a wizard's tower. Maybe it's abandoned because the wizard was killed or imprisoned elsewhere and his tower hadn't been looted yet, rather than the wizard moved on and took all his stuff with them; obviously I don't know the specifics. Having a spellbook makes as much sense in such a location as having a chair or a cauldron or a lab where magical creatures are dissected. If the party went to a blacksmith's shop, it would make sense for there to be an anvil and iron ingots lying around, right? A spellbook wouldn't necessarily be out in the open like an anvil would be, but it makes sense that the GM would have decided that they existed ahead of time (or that spellbooks had been there at one point, but have since been removed).
BW may not be a game about Evard's spellbooks, but presumably it is a game where NPCs have lives outside of the PCs and therefore, their homes and places of work have things in them. At least, I should hope so!
In fact, the whole reason Evard's tower became a focus of play is this:
The rulebook, in its discussion of "the sacred and most holy role of the players", says this (Revised p 269; the identical text is in Gold too):
Use the mechanics! Players are expected to call for a Duel of Wits or a Circles test . . . Don't wait for the GM to invoke a rule - invoke the damn thing yourself and get the story moving! . . . If the story doesn't interest you, it's your job to create interesting situations and involve yourself.
So at one stage, wanting to get things moving, Aramina's player declared (speaking as Aramina) "Isn't Evard's tower around here?" and then called for a test on Great Master-wise to confirm whether or not Aramina's recollection of the location of the tower of this particular great master was correct. The test succeeded, and so Aramina did indeed recall correctly! And in due course, once Thurgon was prepared to go there - he was worried, initially, that it might be a haven for Orcs (like Dol Guldur or Carn Dum in Middle Earth) - the two characters made the relatively short journey to it, where they found it abandoned. That was the GM's narration, as part of framing.
I regard this as relatively illustrative of how BW handles the introduction of setting elements: you can see the interplay of both player contributions (initial suggestions, which all are obliged to take up if the relevant check succeeds) and GM contributions (via framing, or failure narration - in AW/PbtA parlance these would be soft and hard moves).
Wait, hang on--your ability to choose to act was hampered by a die roll?! That sounds... highly suspect
I don't know what "suspect" means here.
The rule in question is Steel. It is Burning Wheel's version of morale. The GM can call for a Steel check if (i) certain conditions are met (normally involving seeing horrible or unearthly things, or attempting to act in a ruthless or cold-blooded fashion), and (ii) if the GM wishes to. (If the player thinks a Steel check for their PC might be warranted, they are at liberty to suggest that to the GM, but it is the GM who ultimately decides if one is needed - on other words, the GM can always say "yes" ie the character is hardened and ruthless enough to withstand or to perform whatever it is that is at issue.)
When Aedhros attempted cold-blooded murder the GM called for a Steel check, and I failed and hence Aedhros hesitated, giving Alicia sufficient time to use her Persuasion spell to convince Aedhros not to perform the murder.