I found it easy to diagnose holding the brakes slightly, almost letting the car go. I had a serious vibration on my W216 with an M273 engine. Since then I’ve replaced both engine and gearbox mounts. The thing that was not obvious to me is that the engine flexes MORE with new mounts than with old ones, which was counterintuitive to me. The idea is that new mounts have oil and all the dampening stuff inside, which lets the engine flex slightly, but the mounts are reducing all of that vibration to pass onto the body. While old ones had an oil leak, which made them brick-sturdy, and that made the body vibrate most.
Obviously when I say flex, that does not mean the engine jumping out of the engine bay, but definitely there was noticeably more engine movement after the service was done.