Weather Kit REST API doesn't contain SF Symbol name.

I think you have to do it yourself. This enable you to use your own images.

This property exists, but it's not where you might expect. See CurrentWeather.symbolName, DayWeather.symbolName, and HourWeather.symbolName. It is not on WeatherCondition, because the time of day matters.

You say this property exists, but it does not, not the Rest API. So the question still stands. I could spend hours and hours trying to guess what symbol to use. It seams like someone out there has something we can use for this.