2003 Grand Prix rear noise, new bearing, new linkage, banging noise and wheel has a play, trailing bars look solid. What can be?

Could be rear wheel bearing is worn .
May need to be checked and replaced .
Does it vary depending on speed

I have 2003 one problem is sway bar and I do see on others broken mine has left the side.

Could be CV Shaft or Hub Bearing as well. Jack up the front of the car, support with Jack Stands and check for play in wheels/hubs/bearings/linkage by grabbing wheel at 3 and 9 o'clock positions for tie rod ends and steering linkage, then 12 and 6 o'clock positions for bearings. You should barely be able to feel play. If you think it is more than acceptable climb under the car while someone else performs the tasks above. Turn wheels for excessive brake noise or out of tolerance discs. Out of tolerance discs will cause premature brake wear and cause pads to move around in the caliper sometimes before starting to grind. Finally, and what I think you're hearing/feeling is the CV Shaft. Grab shaft, move around feeling for excessive play in joint or splines on each end. Turn steering all the way lock to lock and turn wheels at each lock, forward and backward, feel/listen for clicking/popping. Most of the time you can quickly easily diagnose bad CV Joints in a parking lot by slowly, safely driving in a circle forwards and backwards making the joint noise more pronounced. If it is a CV Joint, my advice would be to spend the extra few bucks and replace the whole shaft while you're there. Its quicker and easier requiring less specialty tools to complete the job.

I change both wheel hub bearings when one goes

Doesn't matter what stabilizer does--- the bushings need
to be done-- so you say

Maybe you replaced the wrong drive axle

Put the front tires on the back to see what happens

check the sway bar links

You have been able to narrow it down to a suspension/drivetrain issue, now it is most likely 1 of 2 things. Since you say it is on left rear wheel, odds are you are looking at a wheel bearing, usually this makes more of a light grinding noise. Either way, it can be checked. Lift vehicle up so that the tire is barely off the ground. Grab a hold of the tire and wiggle it up and down, left and right. This should make no noise at all. If it does, you need to replace wheel bearings. 2nd option is it is one of the u joints in the drive shaft. crawl underneath with the wheels blocked, and shake the drive shaft. It is normal for it to move toward the transmission but not normal for it to move up and down, side to side. once again, when you move it, you may hear a clunk, this means the needle bearings inside of the u-joint caps are toast.

By rear stabilizer, do you mean trailing arm or sway bar? If you have a busted trailing arm, I highly advise against driving. This is the bar that runs from the wheel hub transversely toward the front of the car and attaches to the frame. However, a busted rear sway bar, which runs transversely across the vehicle and runs along side the leaf spring, isn't as severe of an problem. You will just run into spongy turning issues.

the rear hub and wheel bearing assembly is sealed-for-life and must be replaced as a unit. it is secured to the knuckle w/ 4 bolts. then maneuver it out through the brake caliper bracket.

Might be a worn drive shaft linkage at the rear axle (differential). Could certainly be a worn wheel bearing.

How would changing the rear pads fix a noise in the front? Take the front wheels off and look for excess rust on the discs or grit in or on the pads. It sounds like you might be competent enough to take the calipers off (it's not very hard). If the noise gets louder with speed, it could very well be the bearings. This is much harder to do yourself (yay FWD), and you might want to get it towed so you don't damage the hubs, etc. Just shaking the wheel probably isn't enough to diagnose bad bearings.