To make the plug work when the Smart Plug is electrical

There is an analog button in the bathroom.
The buttons are connected to the ventilator.
The ventilator is connected through a smart plug.

Then

The ventilator does not work when the analog switch is turned on.
The default setting for Smart Plugs is Off.
Can you make the plug work right away according to the analog switch?
I use Xiaomi Smart Plug(ZNCZ02LM).

I’m not entirely sure I understand your set up, but I think what you have is effectively two switches in series. So electricity can’t flow to the device until both switches are closed.

Like the top diagram here