With summer and the ability to drive with my windows down, I noticed a lot of noise from my tires (Cooper Discoverer A/T3). I also noticed the tires were wearing unevenly in front, so I figured my alignment was wonky. I've done quite a bit of off-roading and just driving on super rocky/bumpy roads the past couple years without an alignment adjustment.

Took it to a local Brakes Plus because it's just an alignment, right?

They told me they couldn't align it because, "Steering rack has quite a bit of internal looseness causing steering angle to be off and tire wear, needs the rack replaced before a proper alignment can be set."

I haven't noticed anything specific about the steering feeling funny until now. Since I got it back, I have noticed a definite "wobble" at highway speeds.

So my question is: How can I verify there's an issue with the steering rack?

I'm inclined to DIY, and typically use OEM Toyota parts, so I'm leery of ordering $700 worth of parts and spending my weekend under the truck if it's not really necessary.

Get under the truck have someone else turn the steering and see if there is movement. New bushings could remedy that. Inner tie rods could be shot also kind of pricey I think around 80 bucks a piece. Steering rack guide could have loosened. There is a very specific way off tightening that in the fsm.

edit: A second opinion wouldn't hurt.

Lay underneath and look at the steering rack for movement while someone else turns the wheel lock to lock. Pay attention to the steering rack bushings. Mine are wore out and cause a lot of feedback in the steering wheel when I hit bumps. Jack the front tires off the ground and grab the tire at 3 and 9 o'clock and wiggle back and forth. You will have some movement, but it shouldn't feel like a click or pop movement. It would probably be helpful to have someone in the cab to brace the steering wheel still while you wiggle the tires.

Get the truck in the air, remove at least the back half of the skid plate, with that off you’ll have easy access to look at the rack. I had movement from my rack and replaced the bushings with Poly and it’s great. The bushing in mine were so bad the rack would move left and right, we could actually move it by hand. Energy Suspension bushings we’re like $30.00.

^^^What they said.
You can also reduce some of the free play by adjusting the steering rack guide. Some replace it. IIRC, there is an early version and later version.

rack guide replacement.