Starlink follows the common solution of having them deorbit and burn up in the atmosphere at EOL. Competitors likely will do the same.

Traffic management is an ongoing debate with the current solution simply being ground based tracking and orbit management.

How would that work? A rocket launches into orbit an unmanned satellite capable of autonomously intercepting the orbit of debris in order to collect it and then deorbit itself? Seems extremely expensive for little benefit.

It's my understanding that atmospheric drag and orbital perturbations due to the gravity of other celestial bodies cause satellites to need station keeping maneuvers just to avoid crashing into the Earth. So it seems to me that this debris problem will eventually take care of itself.

Until your space roomba hits space debris going the opposite direction and becomes even more space debris