SW4STM32 and SW4Linux fully supports the STM32MP1 asymmetric multicore Cortex/A7+M4 MPUs

   With System Workbench for Linux, Embedded Linux on the STM32MP1 family of MPUs from ST was never as simple to build and maintain, even for newcomers in the Linux world. And, if you install System Workbench for Linux in System Workbench for STM32 you can seamlessly develop and debug asymmetric applications running partly on Linux, partly on the Cortex-M4.
You can get more information from the ac6-tools website and download (registration required) various documents highlighting:

System Workbench for STM32

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MAC Address

I have not done an Ethernet board, so I don’t have detailed answers.

The STM device I’m using has a “One-time Programmable” section of Flash, which could probably be used to store a factory programmed MAC for the life of the device.
How to do that will depend on what interfaces you have available. If your board supports a Bootloader, consider using a separate RAM based firmware to program the OTP.