So I did a bit of poking around in the source tree; and on the basis of comparison with some of the other ports, it seems that it is necessary to add:
include("$(MPY_DIR)/extmod/uasyncio/manifest.py")
into:
src/omv/boards/NANO33/manifest.py
Rebuilding a firmware version with that change seems to be give me a functioning uasyncio module on the nano 33. At least, the attached (slightly adapted) aledflash.py (1.1 KB) demo seems to run OK.
Of course it is possible that including uasyncio in the firmware build may cause some other problems, but there is nothing obvious on initial testing. So it may be worth considering just merging this change into the official distribution for the nano 33…