Using raw predictors in
bsts) has the advantage that your counterfactual predictions automatically inherit the seasonality structure contained in your predictors (e.g., day-of-week as well as seasonal effects throughout the year and their interactions).
Deseasonalizing your predictors, on the other hand, can be a useful strategy in cases where seasonal variation dominates all other features in your predictors, making it potentially harder for the regression component to find the right combination of predictors. In this case you'll want to include an explicit seasonal component in the model (using
bsts()). See the documentation for details.
Unless you have too many predictors you could also consider using both raw and deseasonalized regressors and let the model decide.