We have a water treatment system that injects diluted chlorine into the piping when there is water flow detected. I used The Google to search for "water flow switch" which returned many results. I discovered that these switches are used for salt water pool systems as well as drinking water treatment systems.
The switch in our system is a vertical pipe in which gravity causes the "trigger" device to settle over the opening in the pipe. When water flows, the disk of the trigger lifts to the top of the enclosure, allowing water to exit at 90°, while simultaneously placing a magnet within range of a reed switch, triggering the pump.
For your application, if the switch you select does not have Normally Closed/Normally Open options, you may have to use a relay for pump control. That's a minor consideration, but is another point of failure overall.
One of the items (Amazon) from my search uses a hall effect sensor with a small propeller within the coupling, reading a magnet on one of the blades.
This type of switch would require a circuit to recognize the signal (or lack of) and trigger accordingly which could be accomplished with an Arduino or similar small-board-computer.
Coincidentally, I later searched for a booster pump to be able to wash solar panels from the ground. Amazon sells a booster pump to run on 110v house current (USA) and incorporates the switch noted above, which makes is a "turnkey" purchase, a stand-alone system that will likely perform as you've indicated.
