@Charlaquin Thanks for the detailed reply! I think we mostly have a pretty good handle on the differences between our styles as they relate to the examples of knowledge checks at my table. I've excerpted a few of your statements where I want to follow-up, but if I overlooked something you wanted a reply on, please let me know.
What I see as the difference between our approaches to 3 is that in your approach the player is asking the DM if their character has certain knowledge and if they do, to leverage it to achieve a desired goal, whereas in my approach, they are declaring that they have this knowledge and intend to apply it to achieve a desired goal. Perhaps a subtle distinction, but I think an important one as I believe my approach maintains a better flow of the basic pattern of play. Ideally, in my view, the pattern of play should stick as close as possible to what is described in How To Play:
1. The DM describes the environment
2. The players describe what their characters do.
3. The DM describes the results of the characters’ actions, then starts the process over from 1.
Players asking questions does not fit this pattern, and interrupts its flow, so should be kept to a minimum. Ideally, the players would never need to ask questions, but communication being imperfect, it is sometimes necessary for players to ask clarifying questions about the description. Otherwise, I favor declaration of action with the goal of learning what more you want to know, rather than asking if you know it.
This is definitely a place where our style preferences diverge in practice, even though we both adhere to the pattern of play you describe above. To me the idea that the players should ideally never need to ask questions is entirely foreign, and I'm having a hard time wrapping my brain around it.
I can sort-of see a (super-human) DM being able to accurately predict which features of the characters' immediate environment the players will decide are important, and then providing enough pertinent information about those features that the players don't feel like they need any further details to make a plan. I'm skeptical, though, that in practice one can reliably provide sufficient information without simultaneously providing
too much unless one has perfect foreknowledge of both what the players will consider important
and what they will consider unimportant.
But that only relates to the immediate environment, and in many scenes the immediate environment isn't the focus. As a simple example, in just about any social encounter the focus is going to be on the conversation, but the conversation does not need to relate to the immediate environment. Player questions that are sparked by the dialog may therefore have nothing to do with the up-front description, and thus could not have been avoided by making the description more detailed.
There are also the medium/long-term planning scenes where the players aren't actively interacting with any part of their immediate environment at all (except each other). If the PCs are having an IC debate on which of their competing priorities to focus on next, in my experience there's going to be a
ton of background questions for the DM as the players figure out their characters' strategy, none of which relate to the description of whatever room the scene is taking place in.
Finally, plenty of scenes are player-initiated, where the DM simply can't know in advance what will be important or sometimes what the scene is even about. As a trivial example, the DM may be expecting to gloss over making camp one night, but the players turn it into a full-fledged scene, asking detailed questions about the terrain for laying out camp and questions about the varieties of local game available (since different types of game require different hunting strategies).
In all of these cases I see the players' questions as fantastic--they're telling me what is important to them, and showing where they are engaged with the game. And I don't see these questions as outside of the standard play loop--I just see "DM describes the environment" as an interactive process.
Interesting. I guess where my perspective differs is in the idea that a randomly triggered encounter or complication is “created” where it hadn’t existed before. In theory, any such randomly triggered event is one that should be possible in the context it occurs in. There are rats in the dungeon, so randomly determining that the party encounters a pack of rats doesn’t seem to me like creating rats where they didn’t exist before, it’s just randomly determining when and if the characters come across the rats that definitively exist there.
If it helps, I tailor my complication tables to the locations where they are going to be used. I’m not just rolling on a generic random encounter table, and I may not even roll to determine the encounter at all. Rather, I’ll have a list of complications that are appropriate to the dungeon, and when the tension pool indicates that a complication should occur, I will choose a complication I feel is most appropriate to the current context. Maybe I’ll use a dice roll if there are many equally-appropriate options. But to my mind I’m certainly not creating events at random, I’m randomly determining when events that are likely to occur in this dungeon do so.
The tailored tables definitely help. But if I decide to take extra time to try again to pick a lock, and as a result the tension dice pool becomes full, I can see that any unwelcome result was caused by the decision to try again to pick the lock. So if the tension dice dictate that when I get the door open there is an aggressive swarm of rats behind it, I'll know that had I gotten the lock on the first try there wouldn't have been any rats. Thus, the lockpicking attempt "created" the rats. That rats are entirely plausible helps a lot, but I would still personally find it damaging to my immersion.
I think I get it. It sounds to me like what you want is for those random encounters to be drawn from the ranks of the dungeon’s inhabitants, such that if you encounter 3 wandering Kobolds now, there are 3 fewer Kobolds in the barracks when you get there later. A lot of old-school dungeons worked that way. That I can totally understand, although to me it seems like there’s no way as a player you would be able to tell the difference.
If I can't tell the difference, great.

But not being able to tell the difference also means I can't know that an immersion-damaging (to me) mechanic is in use. Random encounter clocks are often advocated as a pacing tool, and they're ineffective in that role if they simply make an upcoming encounter happen earlier. Heck, if the clock doesn't "create" new monsters, a party could game a random encounter clock by fortifying a position and then running out the clock deliberately to make the monsters come to them. So where such clocks are in play, I've seen then explicitly advertised as having the potential for "new" encounters in order to create the incentive not to dawdle.
Where you’re losing me is with the implicit assumption that because the tension pool was used to determine when an encounter happened, that the tension pool must have been used to determine whether or not the creatures involved in the encounter exist. Clearly those creatures must exist in the dungeon, otherwise you wouldn’t be able to encounter them there.
Does my example above with the locked door with a rat swarm behind it as a result of the tension dice provide more clarity? All I know is that the rat swarm would not have been behind the door, but for the roll on the tension dice. The presence of the swarm is abstractly related to decision to take each of the actions that led to the accumulation of tension dice. I'd find that problematic immersively because it wouldn't make any sense to me why each of those actions led to rats where there otherwise wouldn't have been any rats.
By contrast, I'd be totally fine if you said that taking more time to pick the lock might result in a higher likelihood that the patrol (that we already knew about) would stumble across the party, and then accordingly increased the odds when determining whether the patrol actually finds us. It wouldn't cause any difficulties for me with immersion.
(And just to be clear, I'm only explaining why your tension-dice mechanic would make it more difficult for me, personally, to maintain immersion. It sounds like a great mechanic even though it isn't to my individual taste.)