in specific words do static features need a specific data type ?

I think you need to encode that information as numerical values. You can add an exogenous variable (e.g. a binary column) to indicate if a day is a working day or not. You need to add it both to the historical data you'll fit and to the future dataframe you'll use for prediction. Since you need this information for each time point, it's not a static (time-invariant) covariate.

yes but in ml forecast there is no exogenous variable