Action resolution is for resolving actions. It's not about making decisions (except in specific cases where it specifically is). Deciding to sneak by the guard is not the same thing as resolving the attempt to do so.
I find this a strange statement. Action are what drives the fiction -- nothing else does except, perhaps, a GM just telling you a story. And, I agree, the decision to sneak past a guard is not the same as trying to do so. However, in game, as a GM, I really don't care at all about your decision on what to do because I do not adjudicate that and the fiction in play doesn't address or reflect this. Only the action to do so actually matters in play.
And, if the action is being tested, and the GM isn't using Force to drive to a desired outcome, then we have failure and wrongness in action resolution -- I don't necessarily have to add it in prep (you can, no doubt, but you don't have to). By not using Force I mean that the GM will narrate a failure state for the action on a failure and a success state on the action if it succeeds and not have those be the same because the GM wishes the action to succeed or fail.
For the guard, let's say the player decides they want to sneak past. Cool, I don't have anything to do with this as a GM and it doesn't task me to narrate new fiction. What does is when the player starts declaring actions for their character to actually do the deed. Likely, there will be a few actions declared that I let auto-succeed, like moving through the town to where the guard is and taking up a starting locations. This is action resolution, even if it's usually handled very informally, because the GM has to decide if it occurs like asked or if mechanics need to be involved or if it fails due to notes or whatever. Then we get to where the PC ties to sneak past the guard. However the GM chooses to adjudicate this (multiple rolls, different ability checks for different parts, one roll, whatever), the crux is that the fiction that occurs on a success will be different from the fiction on a failure. You might use succeed at a cost for the fail state, in which case the fictional difference is the cost. You may use a hard move and have a failure be discovery and an alarm, or some state between. What should NOT happen is that the fail state and success state be the same. That's an example GM Force -- the outcome is fixed regardless of player input.
So, yeah, I don't follow you when you suggest that action resolution cannot result in failures, mistakes, or being wrong (in the case of attempted social encounters, or trap disarming, or knowing something, etc). Action resolution is a great tool for finding out PCs are wrong or have made a mistake. It doesn't have to be written in the GM's notes (although that's a perfectly valid approach).
The only way it has anything to do with making a mistake is if the PCs don't want to fight the guards, or if they would prefer to enter quietly. There was some discussion as to whether it was good scenario design to have the fight at the gate look impossible, or whether it was attempting to guide the PCs to a preferred alternative; my position is that it can be good design, and it doesn't have to involve any GM preferences, but it could be bad and there could be some rails coming into play. The only relevant mistake to be made would arguably be a failure to look for the sewer entrance if the PCs wanted to get in without interacting with the guards on the gate.
I think a lot of people have said it could go either way depending on circumstance. And, I don't see how it's the player's mistake if the GM frames only the gate and doesn't provide indications that the sewer might exist. That's a GM mistake. Not a horrible, end of game, terrible no good one, but the GM is responsible for outlining the basic options of play in scene framing in 5e. This is a critical duty because the players cannot introduce new fiction, only the GM can, so it's the responsibility of the GM to make sure relevant fictional pathways are at least available through foreshadowing even if not immediately presented as obvious. Failure to do so means the players are not in the position of having to guess if there's another route the GM has prepped at all times because the GM will not present it unless you ask the right questions. I get that a lot of people play this way, and that's fine, so long as they're having fun doing so. However, fundamentally, when you look at the roles and authorities of the GM, this is only ever their fault, even as it's often placed on the players for not being thorough or asking the right questions.
Oddly, I think this is much less true to not true at all for other games so much as it is for 5e (or other D&D). The more the players can propose new fiction and the more the GM is constrained in resolution of action declarations, the less necessary it is to provide the options in framing. I could frame a heavily guarded gate in other systems and be comfortable not providing any other avenues because the players can create them with action declarations. I can challenge those through action resolution, but if they succeed, that fiction is true. If not, well, it's not true, or at least not true they way that they wanted.
