I want to build a smart locker using this part https://www.aliexpress.com/item/32845920160/32845920160.html and a CD74HC4067 multiplexer. Essentially I need to turn on only one lock at time using a relay. I have seen that the lock draws 350mA @ 6 V. Am I risking to burn CD74HC4067 chip? Do you know if there is a multiplexer with higher currents than this?
The 4067 is an analog multiplexer, not a power switch. It is not designed to supply any significant current to its outputs -- the datasheet specifies an "absolute maximum" of:
DC Output Source or Sink Current per Output Pin: ±25 mA
This is because its intended application is for switching analog signals to high-impedance loads, like operational amplifiers or DACs.
A MOSFET or relay would be a more appropriate choice here.