Hi,
The rack and pinion gear shouldn't move. If you want to confirm tightness, I attached the manufacturer's torque specifications below for mounting.
Now, my first thought is you have a worn tie rod. It could be an inner or outer tie rod. If you lift one front wheel off the ground, place your hands at 3 and 9 o'clock and wiggle. If there is movement, have a helper watch under the vehicle to see where the movement is coming from. If it is a tie rod, here is a link that explains in general how one is replaced. You can use this as a guide.
https://www.2carpros.com/articles/tie-rod-end-replacement
I hope this helps. Let me know if you have additional questions.
Take care,
Joe
See pic below.
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Saturday, January 22nd, 2022 AT 10:41 PM