Hi Ben, I just wanted to add this here - but as you mentioned, there is no out-of-the-box functionality in GoodData Cloud to store the last filter value used by a specific user and display it by default the next time they open the embedded dashboard.
It may be possible to implement some custom logic in your embedding application to track and store the user’s last filter selections, and then pass those values back to GoodData when the dashboard is loaded again.
However, this falls out of the scope of the GoodData Support. So if you would like to learn more about if this is possible I would like to suggest you reach out to your Account Owner who can discuss this with the Professional Services team, who might be able to help.