How to pass a list of IDs to MySQL stored procedure?

You should be able to use MySQL’s FIND_IN_SET() to use the list of ids:

CREATE PROCEDURE `get_users_per_app` (id_list TEXT)
BEGIN
    SELECT
        app_id, GROUP_CONCAT(user_id)
    FROM
        app_users
    WHERE
        FIND_IN_SET(app_id, id_list) > 0
    GROUP BY app_id;
    ...