Not turning off fan when speed is set to 0%

I have a pump with an optional PWM input connected to ESP via ESPHome. I used Speed fan as a choice of component as it should give me a way to turn off and on via Relay + set speed via PWM pin.
The pump has special function which I would like to preserve. When the PWM signal is 0, the pump returns to preconfigured state - keeping the constant rate of flow.
The problem is, when I set the speed percentage on a fan card to 0% it automatically turns the fan off.
I did set up

        output.turn_off: relay_2

option to be able to turn off and on the relay when turning off and on the fan…

Is there a better way of controlling such device? Or making the Speed fan not turned off when speed percentage is set to 0?

Set a min_power more than 0%?

  - platform: ...
    id: my_output_id
    power_supply: power_supply_id
    inverted: false
    min_power: 0.01
    max_power: 0.75

Hey veli, thank you for the answer.
I need to be able to set the PWM signal to 0, so that the pump can resume it’s normal operation.
I’m thinking about splitting the device, and not use the fan component, but pwm + a switch and then somehow combine them in home assistant entity card…
Which is a pity, cause it was quite useful to have it as single fan component.