I also don’t know if there is a blanket ban in NSW strata. Assuming there isn’t anything specific to strata, then washing cars on a hard surface with soap running into stormwater drains might well be contrary to state or local council regulations for anyone.
A common owners corporation rule/by-law/article is a catch-all requirement to comply with any law in force in the relevant location. So, it might be enforceable by that means or by just phoning the council and asking them to advise the OC in writing if it would not be permitted.
Does the OC have a grassed or gravel location where car washing could be permitted? Obviously there is demand for somewhere to wash cars. Perhaps people are washing on the carpark because they think they should not drive onto the grass to wash their cars. If that would risk creating an ugly track, perhaps two neat strips of pavers or concrete could be put down to designate a one-at-a-time car-washing spot? Perhaps uphill of a garden bed that could do with regular watering?