This is on the hardware Link, to double check?

Okay, so here's the findings:

1. The Gamesir Supernova in PS4 mode sends a hard-coded serial number. For every single Gamesir Supernova. Moreover, it reports itself as an actual Sony Dualshock 4.
   
2. This seemingly causes Linux's hidraw API to see two Supernovas in PS4 mode as a single device, presumably because the DS4 could be enumerated more than once (if connected via both Bluetooth and USB). I can reproduce this on modern Linux desktop (on multiple distros), where plugging in two Supernovas will only show one, and then unplugging the working/seen one will show at a hidraw layer as (for instance) /dev/hidraw7 disconnecting and then immediately reconnecting, even though it's now the other dongle.
   
3. While other Gamesir controllers in Xinput mode act like Xbox One controllers, the Supernova acts like an Xbox 360 wired controller. SDL3 was only set up to look for Gamesir controllers as Xbox One controllers, and Xbox 360 uses a different USB interface subclass. As a result, when in Xinput mode, SDL3 did not see it as a valid controller.

Item #3 is a super-easy easy fix (just adding the Gamesir vendor ID to the 'valid Xbox 360 controller providers' list, in addition to the Xbox One controller lists), so that's been made in SDL3 now and the Supernova will work in Xbox mode on the Link in the future.

I will also look at the general Linux issue later; if it's an easy fix I can at least make it for the Steam Link, so that the PS4 mode works (and thus gyro) for more than one Supernova connected at a time.

But the more immediate fix will be "use it in Xinput mode" when the next Steam Link firmware gets pushed. Hopefully that helps!