Add an extra field to BuddyPress activity form

First of all, there is only 1 $accepted_args, not 3, so the add_action is:

add_action('bp_activity_after_save', 'where_activity_from', 10, 1);

Second, the value in your tags input is never parsed by BP_Activity_Activity->save() so how could it be part of the array available thru the hook?

Try using the $_POST array, like this:

add_action('bp_activity_after_save', 'where_activity_from', 10, 1);
function where_activity_from( $activity ) {
    // write_log( $_POST['tags'] );
    // do something with $_POST['tags']
}