Hello,

I have a post category called (Anonymous posts) and a user called (anonymous), If any logged in user select the category (Anonymous posts) and publish, then automatically change the logged in author to another author called (anonymous).

This change should only occur upon clicking (publish) and should not occur when post is saved as (draft)

This is an edited example from your code

 /**
 * Update BuddyBlog Author when a post is submitted in a specific category.
 */
add_filter( 'bblpro_post_submission_prepared_data', function ( $post_data, $cat_id, $post, $is_submission ) {
	// update author if the category was selected. Don't do anything on edit.
	if ( $is_submission && 1487 === (int)$cat_id ) {
		$post_data['post_author'] = 4766806;
		// keep current user data for future?
		if ( ! empty( $post_data['ID'] ) ) {
			update_post_meta( $post_data['ID'], '_bbl_original_post_author', get_current_user_id() );
		}
	}
	return $post_data;
}, 10, 4 );