We had a similar scenario at my workplace. For sustainability reasons water for only available in the patio area for 10 mins every other day so we used those 10 mins to fill a 75L water tank and then used a pump to provide water to Farmbot.
However, the water pump was in addition to the solenoid… i.e. it was added to one of the accessory ports. The watering sequence is turn on pump, wait a couple of seconds, open solenoid, perform water sequence. Turn solenoid on/off as appropriate during the water sequence but keep the pump on to maintain pressure. Once the water sequence is complete, turn off the solenoid then turn off the pump.
I had a look at your pump and am not sure if it will be good enough. The only spec it gives regarding pressure is a flow of 5.5L/min which calculates to 330L/hour.
The pump I used is https://www.amazon.ca/gp/product/B07CCH97HH/ which has a flow rate of 1000L/hr and a lift height of 7m. Don’t expect a high pressure shower… but it worked well for us.
We also have a similar bilge pump, but the issue is with pressure. If I recall correctly, the required pressure is 15 psi. However, we’ve conducted some tests with a pressure pump (130 psi), and the water flow is more than sufficient. In just 5 seconds, we get 300 ml of water. If it were any more than what’s needed, we’d risk flooding the entire garden if we allowed it to run for too long.