When using a UL1077 breaker as supplemental protection to a circuit that never leaves the control panel, does the wire on the load side of the UL1077 breaker have to be sized to match the main OCP ul489 breaker rating.
ie: 20A main for a control panel does the wire to the PLC, ethernet switch DC power supply any of that equipment also have to be #12 or can it be smaller and sized to the UL1077 supplemental protection

 

A UL1077 breaker is considered supplemental protection and does not replace branch circuit protection which a UL489 breaker provides. If the UL1077 breaker feeds a PLC, Ethernet switch, or other low-power control panel components, you can size the wiring based on the load and the UL1077 breaker rating, not the UL489 main panel breaker. If your UL1077 breaker is 5A, then the wire only needs to be rated for 5A.

In case you want to make an ESP32 PLC with 8 digital inputs, 10 relay outputs, 4 analog inputs (0-10V), WiFi/Bluetooth, and support for a ladder, MicroPython, and C++, you can see below:

https://www.pcbway.com/project/shar..._4_ANALOG_INPUT_10_RELAY_OUTPUT_43f2ed33.html

 

When using a UL1077 breaker as supplemental protection to a circuit that never leaves the control panel, does the wire on the load side of the UL1077 breaker have to be sized to match the main OCP ul489 breaker rating.
ie: 20A main for a control panel does the wire to the PLC, ethernet switch DC power supply any of that equipment also have to be #12 or can it be smaller and sized to the UL1077 supplemental protection

No, the load-side wire of the UL1077 breaker can be sized based on the UL1077 breaker's rating, not the main UL489 breaker. As long as the wire is properly rated for the load and the UL1077 breaker provides appropriate supplemental protection, you can use a smaller gauge suited to the specific equipment requirements.