Yes, you safety or emergency stop should interrupt the AC line voltage.
Alhough this
https://www.electro-tech-online.com/custompdfs/2011/01/Interfacing_Safety_Relays_Rev04.pdf pertains to AC drives, it does illustrate the principles involved when safety is involved.
You really need to do a "risk assessment" to determine what might happen if, for instance:
1. The motor controller fails to stop with the inhibit circuit
2. Is a breaker for the AC power sufficient for an E-stop
3. What SIL level is required.
4. Remember that if you use a relay to interrupt AC power that's spring returned, the contacts can weld together.
5. What happens in a power fail response. A proper Safety Instrumented system would say use a Start/Stop station and actually monitor that the contacts did actually change state.
6. Electrically tripping the AC breaker (shunt trip) with the Estop might be an option for you. These are special breakers. Usually you connect the switched power to the trip terminal on the breaker. The breaker will trip and remove the source of power to the trip mechanism.
Sometimes you don't want the safeties to fail. I know. I designed a system that worked properly when the lab blew up from a Hydrogen explosion. There was no fire, per say. The actual failure was a excess flow valve for the Hydrogen delivery system that made the operator think that the tank was empty. So 1500 PSI of Hydrogen was released into a line rated for vacuum. This caused a total re-design of the gas delivery system for all gasses and even the times that cylinders were changed had to occur when the building was empty. Some gasses required the use of an SCBA (self contained breathing apparatus).