Tiaral

magical drugs or collars that guarantee the loyalty of these slaves

There's probably an entire industry dedicated to this. Children go to universities or slave-trading courses, where they learn to brew drugs and design devices. Factories in the city supply millions of slaves with their devices. Some of them are exported to other countries. Each slave is equipped with a device as part of the purchase by another person. Newer models of the master's bracelet can be configured using voice commands to control the frequencies of up to ten slaves at once, so you don't have to control them all individually.