I wonder if it would be worthwhile to try and track when it changed over. I know my '03 has the "A/C OFF" display on-screen (the button itself has a snowflake symbol on it - at least until the paint wears off...lol. )
Of course, GM probably changed mid-year, whenever that was, using leftover parts from the prior MY until they ran out of the 'old' ones.
If I'm not mistaken, the same units were used in the pickups & full-size SUVs; those might have all changed in the same MY.
Mine only moves one degree at a time, as well. Even worse, when I first turn the knob after having been sitting 'idle', the display actually indicates the temp is moving in the *opposite* direction as commanded.
Took me forever to break the habit of thinking I was turning the knob incorrectly, and just continue on in the same direction; the display reverses itself and starts moving in the desired direction.
Now that I've subconsciously committed that to memory, it's a quirk I'm OK to continue dealing with, since it does a good job of maintaining the temp where I want it, once I set / adjust it. And, yes, if I adjust it again quickly afterward, it does *not* move in the wrong direction. It's as if when it sits 'unused', the knob forgets its reference point (but the system has been maintaining that previously set temp just fine.)
Oh, and yes, this all happens with the passenger side knob, too. And I believe it also happens if I adjust via the steering wheel button (I have the '1st version' SW buttons; GM removed 'fan' and 'temp' from the LH side of the wheel beginning in '04, IIRC)