print quality: z wobble issue
This looks as if there is a side-to-side force being generated as Z is changed.  Ideally, the X or Y position is determined by the smooth rods, which should bear any force, not the threaded rod.  The threaded rod should cause no motion except upward and downward.

If the rod is bent, but the rod is lightly constrained, then the top, being the free end, will draw a circle.  The bottom is constrained by the motor.  The middle is constrained by the nut, so the top would wander.  If the threaded rod is perfectly straight, and the stepper motor axis and the nut are perfectly aligned, the top would spin without movement.

If the rod is bent and the nut is very tight, there may be a twisting force exerted by the nut, which could cause movement.

Everything is a tradeoff between tightness and looseness, between precision components and the reality of alignment errors.

You asked if the shaft coupling is too tight.  Maybe.  Try removing everything except the motor, coupling, and the threaded rod.  Does the rod fall exactly where the nut would be?  If not, it isn't aligned correctly.  Incorrect alignment can be mitigated by a flexible coupling.  It looks like you are using a Lovejoy coupling with a plaster spider.  Depending on how tightly the spider fits, a Lovejoy coupling can be tight or loose.  I see a lot of machines with the one-piece coupling and a spiral-cut joining region.  THis might be a good alternative, but they tend to take up more space than a lovejoy coupling.

Because Z-axis motion is pretty slow, it is unlikely to be a z-axis vibration issue.  You may have changed the resonant frequencies enough to cause some other problem, but I don't think it is related to the problem in the photograph.