Not sure what you are saying there but given the intention is that you do not waste water, the heater will already be full of water so there is no "initial request" with the recirculating pump.
The valve in the return loop - whether a one-way valve or a solenoid valve - is unnecessary as until the pump operates, the pressure is the same throughout the loop and water will not move in either direction.
My passing interest in this discussion is that I have a recirculating pump installed in my office premises to provide more immediate availability of hot water for handwashing and minimise wastage, but I have yet to implement the control system.
As the offices are quite large, the piping is extensive and allowing the recirculation to run continuously (even just daytime) loses all of the hot water. I need to implement a WiFi IOT system (using ESP-01s) to control it as I omitted to pre-install the necessary wiring.