Have you dumped the grey tank? If it is full the sinks won’t drain properly but usually the shower will have water in it before the sinks act badly.
Possibly the drain pipe is plugged, if you can get a plunger, it might get it moving.
Also if the water in the sink is above the level of the air admittance valve be very careful with the air admittance valve, if you unscrew it from the pipe you could get a sink full of water coming out of it. I would suggest you bail the sink before messing with it just to be safe.
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