My K7 and K8 both have the set up you describe. It’s been so long since I touched them, Ican’t comment. I do recall that full choke pull does indeed lift th main throttle bridge ever so slightly open....increasing the idle to about 1500-2000 rpm.
I presume that is just while the choke cable is in the up position?
Do you have to pull it out fully and crack the throttle to set the high idle like on the old automatic choked carbs of the 60s and 70s automobiles?
The spring isn't always strong enough to open the throttle against the cables. If you fully pull out the choke, then open and close the throttle, it will stay cracked open.
It's easier to notice the throttle closing when you push the choke back in. The return spring on mine is strong enough to close it and move the handgrip a noticeable amount.
If I pull my choke out and bump the bars, that's usually enough to overcome any sticking to get the high idle happening.
Then again, it never really gets cold enough here to need full choke, so I've set mine to ramp up before the blades close too far. I just use it to keep a slightly high idle until it's warmed up enough to idle normally, without all the richness of a fully closed choke. Consequence of that is about 3000rpm idle if I ever do need real choke action.