The checked RadRibbonSplitButton doesn't look good and it is not consistent with the RadRibbonToggleButton when hosted in QuickAccessToolBar. This is reproducible when the IsToggle of the button is set to True and the button is checked (IsChecked=True). Also, it reproduces in the Windows11 and Office2019 themes.
To work this around, you will need to
re-template the button when hosted in QuickAccessToolBar.