The stuttering is not obviously caused by GSX but, instead, GSX is the victim of a stuttering induced by another addon that use Simconnect and it's likely sending too many commands in a short period of time.
The stuttering seems to be regular at 1 seconds intervals, further proving GSX is not the cause, because its own animations are otherwise smooth, which wouldn't be the case if the stuttering *originated* by GSX and yes, 1 second is a commonly used update frequency to communicate with Simconnect, but that alone is not saying much, without knowing how much data is being transferred every second.
Since you said it only happens on that airport, this confirms it cannot possibly be caused GSX, since nothing in any of its animations handling has any knowledge of the airport
when I pushback, the stuttering of the tug affects the plane as well during pushback
That's not an indication the stuttering originates by GSX either. It the sim ( using Simconnect ) doesn't call GSX back at the normal frame rate interval because it's overwhelmed with traffic generated by something else, GSX won't update its calculations to move the plane during the lost frames, so it's entirely expected you'll see a stutter because the position wasn't updated for a few frames.
