I bought the GuliKit KK3 MAX and have nothing but good to say about it.
I use it with the Steamdeck via Bluetooth and wired with my desktop. You can also switch out the stupid Nintendo button layout for the normal one. Also, no proprietary software needed to configure or update it.
Was there an issue on the desktop? I just use wired because I don't need my desktop (Fedora) to be wireless.