There is a flat on the shaft, and the lockscrew is on the flat, so I will bet $0.05 that the problem is elsewhere (but still : fix that pinion! You are ~doubling the localized mechanical stress if not fully engaged)
It must be a trick of perspective (or old eyes), but it looks like the rack teeth are a finer pitch than the pinion.
Any chance that the wiring is not 100%? One coil not being driven, bad contact, broken wire, blown driver, .... Measure the resistance of the two coils in the motor after disconnecting from the driver ... they should be a few ohms and equal. Try swapping the X&Y cables around : does the backlash remain on Y?
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