You forgot about Trip!Yeah, Archer's bridge had just three, I think. Malcolm, T'Pol and Hoshi. The only other stations were the helm console and the situation room tabletop display at the back of the bridge module.

Archer had 4 perimeter stations (2 on each side of his chair) and 1 helm console.
https://www.cygnus-x1.net/links/lcars/blueprints/Starfleet-Bridge-Variations/Page_02.jpg
I hadn't really considered the table at the back of the room since it was used more as an information display for briefings than a control console, but perhaps I should reconsider!
Absolutely - I love the shots of continuous banks of screens as it really sells the "control centre" vibe. But I also can't ignore that sometimes wedge sections were conspicuously absent, so here we are...I like the abundance of bridge stations on the Connie. It creates the feeling that you can truly monitor and control every aspect of starship operations from one room, no matter what the mission.

That's an excellent observation! But I think the position of the turbolift is too far back and based on the angle Scotty walks in should be on the opposite side of the existing turbolift (they should be facing each other).
I agree that the holodeck doors need not match or line up with actual doors present in a simulation - in fact I don't think this was ever done in TNG, at least not often.The holodeck doesn't require you to enter through an in-hologram doorway, so, no, no door there.
So Scotty's (and maybe Picard's) route seems to have gone like this

But regardless of where Scotty enters the Bridge recreation, that portion of hand rail (and wedge, presumably) are most definitely absent on the left hand size of the image, as they were in many other episodes of TOS
And since we've gone this far it might as well be mentioned that the set recreation differs significantly in several areas from the original bridge:...there's also a weird separator between each station, and another perimeter console behind Picard where the viewscreen should be. I guess we could always two-wrongs-make-a-right it and throw in the rotating helm console theory, so Scotty and Picard enter from the normal turbolift, the one in the main shot is the TAS door, and the helm is pointing towards Spock's station. I count a mere two direct contradictions of this stupid, stupid theory in the scene.

The chunky separator that @David cgc mentioned is there on the right of the set and pop into shot every now and then:
https://tng.trekcore.com/hd/albums/season-6/6x04/relics-hd-210.jpg
The hand rail next to the engineering station has been rotated approx. 36 degrees (ha!) and now completely blocks off that console. It's also too short of course, but an additional mini-section has been added behind the captain's chair for no particular reason:
https://tng.trekcore.com/hd/albums/season-6/6x04/relics-hd-222.jpg
The steps leading down from the turbolift never existed on TOS and the platforms themselves are also wrong, but at this stage who's counting?

Perhaps we seeing the bridge through Scotty's drunken gaze and that's why the background details keep shifting from scene to scene

Something I will compliment the creators of Relics on is that as many times as the console section was reused for different background shots, they went to the trouble of swapping out the monitor images on the upper section. The main consoles are still the same of course, but I appreciated the broad strokes effort on what was a limited budget.