Sorry but I am not the guy that can help you on your h bridge electronic design.
All my circuit are very simple and basic.
Regarding voltage for latching solenoid operations, in my experience 12v constant are more than enough to operate most of the valve’s, but this is true because I use a battery.
If you use a capacitor the voltage will drop immediately when you open your circuit….
So you need to start well above 12v.
If you want you can find in the market signal relay that can be connected to a Esp gpio for about 1$ each, I think is the simplest and cheaper solution!