Shmacky-McNuts: Thanks, I appreciate it.
SO, I did a simple test with various distros, installing Antimicrox (via apt, dnf or pacman) to check if the controller is detected as such.
lsusb list it as Valve Software Steam Deck Controller but not all distros recognised the controller as a gamepad out of the box.
Those that didn't detected the gamepad:
Live MX Linux 23 with KDE and 6.1.0-10
Live Linux Mint 21 Cinammon with 5.15.0-41
Fedora 38 KDE with 6.2.9-300
Installed Linux Mint 21 on a sd card to upgrade the kernel to 6.2.* version, still a no go
The ones tested that detected the controller as a gamepad just fine:
Live Bodhi Linux 7 with 6.4.7 kernel
Live Manjaro 23 with KDE and 6.5.1-1 kernel
Live MX Linux 23.1 ahs with XFCE and 6.5.0 kernel
It seems that kernels older than, say, version 6.2 lack the kernel driver for the gamepad, although, everything still works as a keyboard input just fine.
Note that I did the tests while doing some other stuff, it's very likely I made some mistakes as wasn't pay a lot of attention.
I'm sure there's some driver for the gamepad somewhere but would be awsome if anyone did a standalone control panel for the controller, similar to what Valve provides in Steam, able to assign various functions to the buttons and touchpads.
I personally use the right touchpad to control mouse movement and left click, while the left touchpad is assigned to scroll and right mouse click. The lack of personalisation is the reason why I stopped using Linux Mint at all.