Apparently from Android 8 onwards the Mi Fit app is not allowed to create a trusted pairing through its application and won't show up as discoverable even with that option selected. There is a way to force it through a dev mode of some sort but I do not recommend that.
As you guessed, you need an extra app and in this case automation app.
MacroDroid is easy to learn and free up to 5 macros. You need one macro
Bluetooth event → Device connected → your car device
Priority mode/Do not disturb → select one of the options - Allow priority notifications or Block all
Name and save the macro