What needs to be done before covering a shared garage wall with plywood from the inside?
Yes, with the diagonal bracing and the uniform horizontal boards of which some were replaced, along with the "paper" that has some missing spots that just happens to be were damaged boards/siding used to be, I would say it is a safe bet that was the exterior of the garage at one time before the neighbors house was built.

If it were my garage and I wanted to put plywood on the inside, I would do so. If an inspector sees it, and cites you for it, then add the firecode sheetrock. Even so, adding a layer of plywood adds another layer of protection between properties.