> Only full screen reflection is allowed, which means I cannot use Keynote in presenter mode and see my notes!
There has never been an option to display a specific window to an external display (which is what the HDMI device will appear as).
Your options are to mirror your MacBook Pro's screen, or extend the desktop.
If you extend the desktop then you can move specific windows into the extended space, to have them show on the extended display. Also, Keynote will recognize the external display and, by default, use it for the presentation, reserving the built-in screen for presenter notes. This sounds like what you want.
Use System Settings -> Displays to setup an extended desktop and see if that fixes your issue.