The right-click mouse gestures in Maya 3d are one example of solving this problem nicely. If you do it at normal speed, you see & select items on the context menus and submenus. But as you learn the gestures that form from making these selections you can execute them rapidly and the context menus don't need to be displayed. It's a perfect example of training you to use an advanced feature with an easy learning curve, then letting the 'training wheels' come off on a case by case basis, no change in settings needed!

Does anyone happen to know of any other applications that use this kind of UI, or even better, a windows utility that adds this kind of functionality across the OS, building custom context-menus for each application?

Command palettes in modern editors (usually ctrl/cmd+shift+p) are an excellent solution to this UX problem imo.

You can discover some functionality you're looking for by searching for it and activating it from the palette for the first few times, and if you find the functionality useful enough you can spend a few brain cycles learning/configuring the shortcut to accelerate it.

I think a similar paradigm can work for gestures on mobile as well. Some master gesture to open up a searchable list of context sensitive commands, and some mechanism to map new gestures to frequently used commands.

"Can you imagine if there was a persistent button at the top of your screen that said “Open Notifications?” "

YES PLEASE! I've had enough of modern design. Text, links, and buttons all look the same. Sub-panels are hidden behind random things in random places and behind random swipes.

We're ready for a renaissance of discoverability in UI.