the way I have learned to check W124 front end is to put jackstands under the control arms and rest the car on them with wheels above the ground - now really wrestle the wheels side to side while checking for play on all 6 ball joints of the tie rods, the passenger side one usually shows up with great slop if the drag link is shot.

As a rule always refresh the idler arm bushings with new lemforder parts and pay special attention to the washer stack - they are placed to level out the ball point position relative to the pitman arm. They should go back exactly like they came out. (its only 1 additional washer though)

The ball joint requires a long 2x4 and some muscle levering the entire wheel up - if the joint moves - replace it. W124 ball joint failure can mean a totalled car if experienced at speed.

The wheel bearings should also be setup correctly with fresh grease to ensure no slop mimics steering wear, The high caster angle can cause the wheels to slop outwards if the bearings are loose.

For alignment - a 2x4 and a jack also work as spreader bar. It works, the idea is to dial in a hair of toe in to keep the car dead straight while driving.

Welp, replacing the left-side tie rod fixed most of the problem, but in true Mercedes fashion, repairing one problem exposed another, smaller one.
It seems my idler arm bushings are shot, as I have a slight (<1 degree) random steering wiggle that only manifests with the wheel dead center. While I was under the car, I noticed the control arm bushings look pretty crappy too, so those may be contributing to the problem.
Onward! :)

idler arm bushings are do-able.... but a bit more tricky..

if i remember... i had to use a tool similar to a dremel..to saw off the nut to the idler arm.... and when you install ....you put the nut and bolt in the opposite direction of the factory install... you will find that there won't be enough room to install the bolt in the factory direction.