Can you break this out into its constituent parts for me? How does this "gestalt-ish vibe" come to be with respect to:
- Distribution of contribution at the table
- Pace of play
- Table-facing vs GM-facing decision-points and action resolution
- System integration (as it relates to the above 3 things)
- GM theatricality and exposition length
- Group chemistry
In general, when a TRPG is going well, there's a feeling that what's happening in the game is more than the sum of the participants' contributions--which is my understanding of what "gestalt" means, though that may be incorrect. That's very much like playing in a band, and the only thing that seems to cover it is "group chemistry," though it's both more than chemistry and not the entirety of the answer to that, either.
Specific to the D&D 5E games I'm running:
Everyone contributes. While I might
talk more than half the time, because of how 5E distributes actual narration, I feel as though I contribute well less than half of the actual fiction that applies in play. Yes, I did most of the world-building (because I enjoy doing it, and because I haven't enjoyed running/pplaying in collaborative worlds as much) but it's possible for remarkably little of the broader setting to be relevant for a given session; and given that I think character and action are a greater part of narrative--and the players are bringing more of those (again, relevant to the story) than I am, I think the distribution between players (as a whole) and DM is pretty even.
Pace of play ... varies. I don't like for anything to take so long in the real world that the players forget why the characters are doing it, so even if the characters are exploring something like a dungeon, or traveling, I try to keep why they're doing it foregrounded some. But if a party is coming up on something that looks as though it's going to turn into a major fight, I don't mind if they take as much time as they need to, to get their plan/s together. Also, there is variation in how quick on the uptake the people around the table are (both person-to-person, and a given person session-to-session).
I frame situations, usually by throwing stinky stuff at a convenient fan. Sometimes a party can choose not to engage that; often they can't. I make an effort to over the course of a campaign provide multiple longer-term goals for the party to pursue (some from their characters' backstories, some arising during play). Decisions as to how to handle a given situation, which goal/s to pursue and how, and such, are pretty much entirely up to the players. You want to go to Auriqua to try to avenge Taman's family's death--sure, I'll work out what's going on in Auriqua and put leads there to get you in the direction of Taman's revenge. Action-resolution is 5E, though I find it efficient and fair to announce DCs for saves (most of the time) and to publicize ACs for monsters after like a round or two. If there is real risk in a skill check, I try to make sure the player/s and the DM are on the same page as far as that, and as far as what success will look like. I use some checks--knowledge-type checks mostly--to see how quickly the PCs can learn something. I don't (much) play NPCs as cagey--there isn't a ton of call for social skill rolls.
I am not entirely sure what you mean by "system integration" in this context. The answer that comes to mind is that everyone at both tables knows 5E pretty well at this point, so there isn't a lot of fumbling in the rulebooks, and no one a the table is likely to be surprised by something lurking in an edge-case. I very much trust the players to know the rules for how their characters work and play by them--I almost never check the players on the rules (in fact, I'll ask about a rule sometimes). I have a sneaking suspicion I haven't answered you on this, which is unintentional.
I am not a theatrical GM. I've worked with (voice) actors--15+ years recording audiobooks--and I know my limitations in that regard. I have a grasp of how to use language, though, and while I can't really do accents I can modulate my voice to convey character. My exposition length varies, I think. I have in the past been pretty explicitly cinematic (referring to something as "having blown the F/X budget," for instance) and I've been known to sprinkle "oh crap!" moments into scenes.
Best I can tell, everyone at both tables really likes each other. Some of the people I've known a while, others I've only known as long as I've been DMing for them. They certainly tend to work well together in-game, and at the table. There might be some variation in playstyles, but nothing that's way out of the norm for D&D, as far as I know.
--I think I might have answered a slightly-wrong question, and described what that gestaltish vibe
looks like at the tables I'm DMing, not so much how it came to be; but I think the answer to that is kinda contained in what I've said. I think it has come to be, because the people at the tables wanted and allowed it to come to be. The players have said kind things about my DMing, and I've been clear--always--that I could not be the DM I am without excellent/compatible players. I'm deeply aware how fortunate I am in that regard.