The SelectionSettings selection.selectedIndex() method currently has no effect for circular charts. It does work for cartesian charts and you can programmatically select a bar, for example.
The example at https://help.syncfusion.com/flutter/circular-charts/methods has several typos in it, but when corrected, the function fails silently and has no effect. It looks like the issue is that _selectionRenderer in selection.dart is NULL for circular charts and so the selectedIndex() function essentially does nothing.