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You can try to use CoreTextEditContext.InputPaneDisplayPolicy property, it indicates whether the input pane should be shown automatically when focus enters your text input control. The default value is Automatic, so the screen keyboard will display automatically, you can set it as Manual, and when you use InputPane.TryShow() method, the screen keyboard will display.
CoreTextServicesManager manager = CoreTextServicesManager.GetForCurrentView();
CoreTextEditContext _editContext = manager.CreateEditContext();
_editContext.InputPaneDisplayPolicy = CoreTextInputPaneDisplayPolicy.Manual;
Here is an official sample about how to control screen keyboard manually, you can refer to it.