I have been catching rainwater and using it between storms to get water down to deeper roots. Many plants survive on on winter rain alone. Since we are under normal where are they going to get it?

Well, the rain is light but has been coming down steady for four hours now. I don't think I'll water any time soon. We also have rain barrels and they are all full now. Yeah!

Wouldn't it make sense to continue watering so that the top layer of soil in some lawns and garden beds doesn't become hydrophobic? I wonder if those city notices are giving the right advice.

The city notices about watering on certain days are designed to be easy for the city to enforce, not designed for optimal plant growth. They are made by bureaucrats, not gardeners.

Deep mulching helps a lot with keeping the surface soil from becoming hydrophobic. Not much help for lawns (I don't have one so no advice from me there), but helps a bunch with ornamentals and vegetable gardens.