Don't have time to comment in deep. So a quick glossary to confirm what I suspect you likely had in mind and a comment or two:
Table-facing procedures: No secret way of doing anything that only the GM knows or comes up with on the spot. Its all there and every participant at the table knows it and all the time. When the state of the game goes from a to b, nothing about that is a mystery. Sable, clear, transparent, out-in-the-open. An epithet you've surely heard is "that is board-gamey!"
If I understand this correctly this can definitely occur in sandbox. It may not occur as it does in the kinds of games you prefer, but I often am very clear about what procedures I am using, how I am making decisions, etc. Even in cases where I have to make up a procedure on the fly my usual routine is to explain that process to the players and ask if they think it would fairly address what they are trying to do (and they often suggest changes that I incorporate). For me this just adds to the sense that everything is above board, and to the sense that the 'physics' of the world are legit (i.e. not just a product of me having outcomes I prefer)
Play Loop: Step 1 > Step 2 > Step 3 > Step 4 > Back to Step 1. Rinse & repeat. While the content of play changes, while the characters change, the stuff you do and who does what stuff repeats. Over and over. Until we're done.
This matches how I have heard the term. I suspect most sandbox GMs would consider this overly rigid. I also suspect you, Manebearcat, might watch a sandbox game and discern a play loop. So I don't know that it is not present or excluded so much as not part of how we conceive of play if that makes sense.
Orbiting Continuity/Canon/Backstory/Metaplots: PC-independent stuff that is ultimately the center of play. At conception of play, this prepped stuff "gravitationally captures" future play. Future play orbits this stuff. "Here is the menu of PC-build or evinced-player-interest independent things to do (hooks, goings-ons, intrigues, mysteries, overarching conflicts, side quests)." "Oh, you declared that action...well let me check my notes to see what happens or whether or not that action is even permissible." Player: "Do I know about <NPC, backstory, faction, etc>?"
I am still not sure I follow this one about orbiting.
There isn't a menu of hooks though. Again in sandbox the idea is you can do anything you want. The GM might provide possible starting points via conflicts that exist, and other details but the players can just press on and push for anything they want (again though usually limited through their characters).
Again the starting points you are emphasizing (which can exist in a sandbox) are largely more what you find in something like a traditional linear campaign or something. You don't push hooks on players, and you don't hadn't them a list. Occasionally stuff like a mystery will emerge I find but more often than not the adventures arise much more organically (and often conflicts are created as PCs interact with NPCs and groups).
I will say if the players declare an action, the action is always permitted in sandbox. What is not always certain is the outcome. They can't declare their action over the setting material for example (i.e. a player can't say "I assassinate the king and take his throne"----he could try to do those things but he wouldn't be able to declare such an outcome in most sandbox play).
The inverse would be content orbiting PC-build or player-evinced-goal/interest.
PC-build dependent: Content that is generated is not independent of PC build or outright spoken player interest. For Mouse Guard, content generated engages with a PC Belief, Instinct, Goal, or Relationship.
This is pretty optional in something like a sandbox. I do sandox+drama, and there is no problem introducing elements that connect to things the players have established about their characters (as an example a player wanted to explore a relationship with his character's long lost father and that became part of the campaign). Some sandbox players and GMs might bristle at this, but it isn't universal. And things like tables can tie specifically to these things. I have grudge tables for example. They are an important thing that makes my wuxia campaigns function and they always tie to things about the PCs (grudges can emerge in game, the player can establish them at character creation, etc).
Economic modeling is a generic stand-in for any preoccupation where game content (and possibly game engine resolution stuff) is concerned with simulating setting stuff that is independent of conflict-charged content that centers around challenging the thematic aspects of PC build or the evinced dramatic needs that the player has declared for their character. Players are going to spend time managing decision-trees/declaring actions, and might even allocate PC build resources, that are the equivalent of sorting out exchange rates for currency or extrapolating granular speed : time relationships for overland travel rates to set up a potential intercept point on a map for a caravan or something. Its the type of stuff and the weight of it upon the balance of play, not the exact example.
I have to be frank and say I just don't understand the language you are using here. So I don't think I can really respond to it in a way that is meaningful or devoid of confusion.
On the Settlement entry above. My guess is your sandbox games don't have 8 of those entries above and that is it. My guess is you have 8 of those entries above + some level of canonical backstory and continuity (likely multiple of these that are concentric or layered or independent from one another) that marches forward through play that is PC-independent + a stable of PC-independent plot hooks/intrigues/side quests/NPC & or Faction arcs.
Again this really varies. Like I said sometimes I have a lot of depth sometimes I have something closer to what you posted. I would say mostly these days my notes are more likely to resemble the example you gave. It can vary though
Things are never independent of the PCs. If the PCs are not engaging a particular area and something is going on there, it may march on without them. But I am usually more focused on the stuff and people going on around the PCs. Sometimes I roll randomly to see what is going on in the broader world or advance the historical timeline, but that still is all stuff the players could potentially influence if they chose to.
For factions I don't usually plan stuff out in an arc of any kind. If a conflict is going on, and the players are totally absent from that conflict, my default is to use tables or to roll opposing dice pools to see what the outcome is (and that stuff usually arises because of what the leadership are trying to do, not because I have a particular arc I want). And a lot of times the reason I even being thinking about that with a given group is because the players interacted with them in some way
You have a fairly high resolution setting conception at the outset of play that is independent of player input and independent of PC-build input and play features players exploring that setting; interacting with people and places and continuity that is related to this stuff that has been pre-generated > PCs going on quests where a sequence of actions and resolution and consequences take place to have this setting stuff change > character advancement > rinse and repeat (except possibly the PCs do follow-on stuff with that setting stuff they just changed because the players have become interested in exploring that to its conclusion).
I don't find this to be particularly the case. Yes there is often established setting material to fall back on for sure (dungeons are a useful thing to just have in the setting for instance). But a lot of what emerges is a result of play, not prep. I will often start with a number of of details hammered out for example. But that isn't a requirement. And the campaign doesn't begin and end with those things. It is entirely possible for example to want to run a wuxia campaign where there are 8 sects I have planned out in advance and the players never interact with a single one of them because they are more interested in exploring things I never thought of.
What I will say is it isn't Hillfolk. The players won't generate that setting material simply by narrating things. But stuff will be generated in response to where they are going, who they are seeking, what they want to do, etc.
Stuff like pre-generated quests are pretty rare for me and I think for a lot of sandbox GMs (this can vary tremendously though). I prefer adventures that arise organically. I don't like handing players quests. Sometimes players may do something that falls into that (i.e. hear about a legendary object and seek it out----and if they do where it can be found is something that would be determined based on either what makes sense or what is established). But those are pretty rare types of adventures.
I will say there are usually concrete things in the setting. But I get the senes that the way you imagine me and my players interact with those things is very different from how we do (a lot of your descriptions of sim play seem to resemble the kinds of adventures I remember being put out in the early to mid 90s by TSR for example, which are exactly the types of adventure structures most sandbox GMs are seeking to avoid).
Now and again, you may have a table to generate something live. But that something generated is, again, PC-build independent (or at least frequently if not perpetually).
Again I may not be 100% sure of what you mean, but this is not written in stone. I often build things around the PCs and connect them back to them. Not every GM does. I think if something like drama is important it is fair to incorporate threads from the PCs. But this is something that I think honestly varies a lot. In many sandbox discussions you sometimes encounter this platonic idea of a sandbox that is so realistic and so focused on naturalism that, for me at least, it wouldn't be very fun to play. I think the vast majority of sandbox GMs consider things like what the player characters were made to do, what types of things the players are interested in doing, etc. This may often need to be framed in naturalism, but it is still there. There are plenty of conceits to playability in sandboxes.
Again I am not so sure. It is possible I am not fully following the language and confusing your points. But if I follow any that I have been responding to, I think sandbox play is a lot more varied than it is being given credit for here (at the very least it is quite different from early 90s era TSR modules)
