Set an external display as main and always display the app switcher UI on it

Solution 1:

The primary display is configured correctly. The app switcher should be shown on the external display, only if the Dock is not set to Automatically hide and show, and is always visible on screen.

Make sure you have not enabled Automatically hide and show the Dock under System Preferences → Dock. If enable, toggle the setting by unchecking and re-checking it.

If you wish to keep the Dock hidden and shown only when the mouse pointer touches the edge which houses the Dock, the app switcher will be shown on the screen that has last displayed the Dock. Thus, to show the app on your main display (external, on visible right), move the mouse pointer to the edge of the Dock, momentarily display it and then use the app switcher with the keyboard shortcut Command + Tab.