I use the H1N, and because it requires me to reconfigure it into audio mode every time I plug it in, OBS has already launched by the time I do that, and I end up having to manually change the audio input capture source to the Zoom all over again. Until I do that, I get no audio. I'm not sure if the same thing would happen if I waited to launch OBS until after configuring the Zoom recorder or not.
I'm guessing all of the Zoom recorders probably have somewhat similar firmware, so you might might need to do something similar.