Hi Robert,
Greetings from Syncfusion.
We would like to let you know that currently there is no support to add star shape as badge icon. We have considered as feature request and can be tracked through feedback portal link.
Please cast your vote to make it count. We will prioritize the features every release based on the demands and we do not have immediate plan to implement this feature since we committed with already planned work. So, this feature will be available any of our upcoming release.
If you have any more specification/suggestions to the feature request, you can add it as a comment in the portal.
Thanks,
Rachel.