From your description, it does indeed sound like you found the cause of the noise, but that type of failure is very uncommon. When the end of the rack has that much movement, it is going to move away from the end seal and allow power steering fluid to leak into the boot. If the boot is dry inside, I can't explain how there can be enough play to result in that noise.
Here's the instructions for removal and replacement of the steering gear. They mention locking the steering wheel straight ahead, but they don't say why. Air bags on the steering wheel require a solid electrical connection. They can't rely on the sliding contact / slip rings we used to use for horns because those could easily have the slightest of intermittent connections just at the instant it is needed. Instead, they use a wound-up ribbon cable in a plastic housing. That's called the "clock spring".
That ribbon cable is just long enough to allow it to wind up fully when turning fully one way, and little more, and to unwind fully when turning fully the other way, and little more. Once the steering shaft is disconnected from the steering gear, if it is rotated just one revolution either way, then reconnected that way to the new gear, that ribbon cable will either wind up too far when turning fully one way, and it will instantly tear apart on the end, or it will unwind too far and fold over on itself. That folding over will occur multiple times over days or weeks before it eventually cracks on that end.
To prevent that potential damage to the clock spring, be sure to start with the steering system centered, then lock the steering wheel in that position until the steering shaft is bolted to the new steering gear, which must also be centered.
Images (Click to enlarge)
Tuesday, January 14th, 2020 AT 12:19 PM