Connecting the pad to a PC has it show up in lsusb like this:

ID 1189:8890 Acer Communications & Multimedia

The keyboard ships with Windows software to do a first time programming of the buttons (links added at the end of this log), after which it should be usable on any device (I did not test this though, I opted for first opening it up).

After unscrewing the bottom which is very hacker friendly, it showed its internals which is just a CH552 and some passives + USB-C connector. The board looks very well assembled with the MCU easily accessible for reprogramming.

To reprogram the chip there are several flashers available, I picked isp55e0 from the AUR. I've read somewhere that the chip should be in DFU mode, and to achieve that I have to boot it while holding D+ at 3v3, which means connecting pin 12 and 16 together. And this board has nice test pads placed next to each other for this! So I guess these pads are there for exactly that reason.

On the other hand, connecting USB while holding D+ at 3v3 sounds like a bad idea to me, so I did not try that yet. I'll do further research on how to flash them first, and report on this in a new log.

EDIT: actually, CH55xduino https://hackaday.io/project/172143/instructions indicates it is really as easy as connecting D+ to Vcc (5V in their case), and then connect USB. Let's try! and expect a new log soon.

EDIT2: so the super easy way of getting into the bootloader (D+ to 3v3 using the pads) is not working, probably because the USB is in the way. Luckily, The Rabid Inventor wrote that there is another way, pull pin 3 to ground, and that works! I can access the bootloader now, and reprogram the chip. Woohoo!

ID 4348:55e0 WinChipHead

http://rabid-inventor.blogspot.com/2020/05/getting-started-with-ch55x.html

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The keyboard seller provided the following link for the Windows software:

https://drive.google.com/file/d/1mnlRUE-Jm86K6dOqlQKTPPNid63T6JTf/view?spm=a2g0o.detail.1000023.1.1ebb1edaXPwpAh&usp=share_link

And Reddit provided some more:

https://www.reddit.com/r/keyboards/comments/u1bfbn/help_looking_on_software_to_program_this_keypad/