Do you think that being "able to make decisions from the perspective of their characters with what feels like the same degree of reliability as the characters would have" is supported by the GM sharing information or hiding information?
In the majority of cases, I think it's supported by sharing information the character would have access to and hiding information the character would not have access to.
Do you think that a GM will typically provide enough information to a player that will equal the amount of information available to a character in the situation they're in?
"
A GM" is extremely vague. Which GM out of the hundreds of thousands are we talking about? I don't know the vast majority of GMs, and it would be nonsensical to try and answer the question without knowing who I'm actually talking about. I would, however, feel confident that most or all of the GMs advocating for living world sandboxes in this thread, who are advising that they are running successful campaigns with something along the lines of that method, are providing
enough information.
As I would hope has been established, no one is suggesting that the information fidelity is anything resembling that which we experience in the real world. I can't describe
exactly how the breeze feels, each and every scent in the air, the exact tint of every colour, the precise tone of every voice. The aim is for the information to be sufficient to allow for informed decision-making and the suspension of disbelief we need to imagine we're in a different role.
What about information that may not be obvious? What about what the character might intuit? What about hunches? How do you allow for that kind of thing? Do you use skill checks or similar? Do you just say something like "something about the way he looks at you, you know he's being dishonest"?
The specifics will depend on the game in question, the character in question and the precise context. It might involve formal rules, ad hoc randomisers, cues taken from the player and/or judgement calls.
It would seem to me that you are placing a priority on persistent immersion in character. That you're perfectly happy with limitations on player agency based on this aspect of play. You don't mind the GM withholding information from you as a player if it's based on the perceived limit of the character's knowledge.
I am definitely OK with limiting
player agency to the control of their
character, from the perspective of that character. I'm pretty sure that's already been established as fairly standard part of the style of play being discussed; everything you're describing here is pretty much pivotal to that kind of play, IMO.
On the odd occasion I'm a player, I'm not only OK with the GM withholding information on that basis, I will generally
expect it, unless it's been explicitly established that the style of play involves a different process.