Indentation mode is not changed for already opened files without reloading them. This is not indicated in the Editor -> Editing -> Indentation or Editor -> Open/Save -> Modes & Filetypes settings.
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Indentation mode changes between 'Tabulators' and 'Spaces' in Kate Settings -> Editing -> Indentation, but changing to 'Tabulators and Spaces' instead changes to 'Tabulators'. I can change to 'Tabulators and Spaces' from the Indentation pop-up at the bottom of Kate. In addition, changing the 'Indentation mode' setting in Kate Settings -> Open/Save -> Modes & Filetypes causes a crash but that's likely a separate bug. KDE Plasma 5.24.6 KDE Frameworks 5.92.0 Qt 5.15.3 Kernel 5.15.0-52-generic
That works as designed, if you e.g. use tab with 4 and indent with 4, it is just indent with tabs. (just as an example)