Embarrassingly, I don't really understand Hyper. I have a Moonlander and AFAICT the firmware (or at least the Oryx configurator tool they provide) says Hyper is just a combination of the basic 4 - Alt+Shift+Ctrl+Meta. I'm pretty sure that's at least not historically true... but I don't have a whole lot of use for it so I haven't tried to wrap my head around what's going on there.
I imagine there's a "real" hyper modifier but I haven't attempted to use it. For my sake, since I use GUI Emacs I find that I have enough mappings without it (I'm also a dirty evil user). A friend makes extensive use of it because he primarily uses Emacs via a terminal and Hyper avoids all other terminal keybind conflicts he might otherwise run into. But, he uses X11, too so no PGTK Emacs even if/when he does run GUI Emacs.
I'll try to dig into this some though and see if I can (a) determine a way to map a "true" hyper to my keyboard and (b) use it in PGTK Emacs and follow up with you.
X11's XKB (which, funnily enough, is also the standard keyboard layout system on Wayland) has support for Control, plus another 5 modifiers. Specifically, I believe Hyper is typically mod3. If you run xmodmap in a terminal under X, you'll see which keys are assigned to which modifiers. I have a custom XKB layout that assigns some keys to Hyper, and then adds Hyper to mod3. With X11 Emacs I didn't have to do anything to get it to work. But I don't think I've ever seen a pure GTK program recognize Hyper, so it may be a GTK limitation.
For learning XKB, I recommend the Unreliable Guide to XKB[0]. XKB is sorely underdocumented, so guides like these are the best way to learn it.
I imagine there's a "real" hyper modifier but I haven't attempted to use it. For my sake, since I use GUI Emacs I find that I have enough mappings without it (I'm also a dirty evil user). A friend makes extensive use of it because he primarily uses Emacs via a terminal and Hyper avoids all other terminal keybind conflicts he might otherwise run into. But, he uses X11, too so no PGTK Emacs even if/when he does run GUI Emacs.
I'll try to dig into this some though and see if I can (a) determine a way to map a "true" hyper to my keyboard and (b) use it in PGTK Emacs and follow up with you.