How does one protect electrical in a 2x4 flat studded wall?
I use these behind large-volume boxes in 2x4 walls, to protect the entry point of the box. They should also work for your purpose. They are 5" x 8" self-nailing steel plates:



The example I got was Oatey 33899, but I'm sure there are other manufacturers. They are cheap (less than $1 each).
An example of a supplier, not a specific endorsement: https://www.supplyhouse.com/sh/control/product/~product_id=33899