I would not assume anything drastic like entire control units. Nor would I expect a scan of the system to tell me what part to replace.
The first thing I would do is just bring the car to a trusted mechanic (if you don’t have one now’s a good time to find one - you want a local, independent shop).
Tell them what is going on. Ask them to inspect and if nothing obvious is out of kilter ask them to just pull all of the connectors for the wheel speed sensors, clean them up really well and plug it all back up. I own a GM of that era and have found the electrical connectors to be the flimsiest and cheapest I’ve ever had on any car. mark9207 is right that the sensors are built into the wheel bearings so the sensors can’t be cleaned. But part of what is inspected should be the wheel bearings. Have all of that checked and see what happens. This could just be the first sign that you need a new wheel bearing.