If you have a 'water panel' with switches/valves........check that you don't have the 'fill' one Open.
If you don't have that set up then water pump internal check valve is leaking thru allowing city water to backflow thru pump.
Turn city water OFF and run pump.....this will sometimes clean and debris out of pump and allow check valve to reset/close.
After using water in fresh water tank shut off pump and go back on city water if you want.
If fresh water tank refills then you can rebuild pump OR just buy a $10 in-line check valve and install it in pump suction line
City water and regulator.......how much pressure is regulator supplying?
Many showers have flow restrictors in them.......disconnect hose from faucet and check for reducer. Check other end of hose at handle or even in handle. Remove it or drill it out to enlarge flow.