OK, I checked bluetooth config again, and you're right, the input module was on ignore list again
I deleted it and keyboard now gets paired again but it works no better than before (bt-hid-scripts still uninstalled).
I played with some different layouts and only one that yet made any difference was layout france: no keys at all working.
I'm just on the verge of configuring that damned stuff with a big bad hammer!

Is there any tool which displays received keycodes / scancodes from keyboard directly so I could at least try to build my own mapping?