First things first, I used this guide to disassemble the motor: https://www.youtube.com/watch?v=ZH6RM_SdRlw. It can actually be quite scary before you get the hang of it. In addition to screws, the magnets lining the inside of the case keeps the two halves together and if you're not careful as you pry them apart they may slam shut again, quite forcefully. In other words, don't keep your fingers (or any other parts of your body) between them until they are completely separated. Use tools for prying!

As a first attempt to attack the rust, I soaked the stator in 5-56 (WD-40 equivalent I guess) and let it sit for a a few hours. This did practically nothing, which shouldn't have come as a surprise.

In my second attempt, I mixed some citric acid with tap water and soaked the stator in it for two days. It shouldn't really take that long, but my solution was quite diluted since I just had a few grams of the acid at hand so the reaction was slower.

This seemed to do the trick. All the rust went away easily with the help of some steel wool, and I washed away all the corrosion and acid with tap water. After that, I soaked the whole thing in 90% ethanol to help drive the water out, and then let it sit in the sun for a few hours to dry. My only worry was whether the built-in sensors and their PCB had survived the acid treatment, but they did just fine.