ABS light still on after replacing sensor

If the sensor was the problem it will clear itself as soon as you start moving and the system runs its testing cycles. That is because the ABS runs testing continuously to detect any faults. If the sensor was not the faulty item the light will stay on.

Not that way normally for ABS. That system constantly scans through itself and if there is a fault the light comes on. Repair the fault and it should go out when the vehicle scans itself again (which with ABS is a constant thing). If it comes back on for the same thing with the same code it was never repaired correctly in the first place.
The normal reasons to get a speed sensor code is a break in the wiring to the sensor due to age and the motion the wiring goes through as the vehicle moves or the connectors get corroded and the sensor signal cannot get to the ABS control module.

A cracked brake shoe/pad would show up as noise and possible a shake when applying the brakes. It would not usually trigger an ABS light. However a cracked ABS tone ring, bad sensor, broken wiring, bad wheel bearing or faulty ABS module can all cause an ABS light. All of which are basic checks a tech should look at if there is a light depending on the code in the system. That is because many of them can mimic each other. For instance a cracked tone ring will show as an intermittent signal, as would a failing wire or loose sensor.

The problem many time is that shops do not keep up with the technology on vehicles. These days there are more computers on board the average car than were on the space shuttle! However, once you learn how they operate and understand that the codes that come up are not "this part has failed, change it" but rather "I see a fault in this system, please check over the associated parts" it gets far easier to do a proper repair. But there are places that refuse to learn the systems or just opt to do what many here call "fire the parts cannon" IE: let's swap any part related to the system in the hope that one fixes it. That gets very expensive and may not actually repair the problem. That is when you get an explanation of "Well we got code P0XXX before and if it comes back it must be something else"

This is one of the things that makes the industry look like crooks. That and the "they do not know what is going on so charge them more" attitude in some shops, being the larger ones. Thing is that doing the proper diagnostics and then replacing the actual faulty part is 99% of the time faster and easier overall. Which also means the vehicle gets repaired and the customer gets a lower bill.

Brake light switch should not cause a wheel speed sensor problem. I would be willing to bet the issue is either the wiring between the sensor and the module or a connector. If they unplugged the sensor and tested at the sensor side connector that leaves the remainder untested.
The fastest way to see if the sensor is reporting would be to put a scan tool on the car select the live speed data from the sensors and drive it around the block. If you are seeing say 25 kph at each sensor then there is an issue with the module. If as I suspect you see 25 kph at three wheels but the left front shows 0 then there is a wiring issue.

Some days I wonder if I should just own a bicycle, then I remember that the closest store is twenty miles away.

That judder would be because the ABS module is activating as you use the brakes. It means that regardless of the sensors reading perfect, the ABS module is not seeing the one that is setting the code. As soon as the code sets it turns the ABS system off and turns on the lights to tell you there is a problem.

Not sure what to say. I just know what I would be looking at as the problem and how I would do it. I would start by connecting a scan tool and go for a short drive while watching the speeds the sensors are sending to the system. Then if one was reporting wrong I would connect an oscilloscope to the wiring at the ABS module and see exactly what is going on.
One of the drawbacks of this type of assistance, I cannot see what they are testing or seeing. Someday there will be auto repair by remote, like they have for surgery.

That would throw the tone ring out of alignment. Sort of surprised they did not see it while doing the other work. Or noticed the issue when they tested the sensors as it would have been erratic. But at least it is repaired.

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