Including identifier in machine learning model as feature vs separate model for every identifier
In my opinion including id as a feature will not make sense at all, because the model will treat the id as a numeric value which will decrease the model performance, because there should be no connection how big the id is and how many customers there are for that id.

Option 2 can make sense if you have enough data for every branch.

My suggestion will be to look deep into your features and try to find a feature which will replace the branch id. Let's say the number of supporting desks in a branch or the location of a branch as a categorical value. If you find enough features that can describe the specifics of branches, then no need to include ids or to do it separately.