I had come across the Solaar before, have not tried it yet. Here's a page, which claims that most Logitech keyboards, in addition to the FN+LeftClick toggling of the tap-to-click feature -- also support FN+ESC to toggle the operation of the F1 thru F10 keys. In the default mode they are sending the media center commands. When switched, they just send the raw F1 to F10 escape codes. I do understand Solaar can control this also, but cool if the keyboard hardware itself can do it with a simple FN+ESC.
https://en.code-bude.net/2017/09/02/cha ... -software/
HOWEVER, when I tried that FN+ESC combination here with my K400+, the Raspberry Pi 4 turned off the display entirely. Window system vanished, stopped feeding display signal, monitor turned off. It almost looked like it went into some kind of Suspend mode. Which is what FN+ESC does on some laptops. I could not get out of it, and had to power down / back up again.
Any idea of what FN+ESC does with Raspbian? I did a bunch of web searches but could find no clues. The page above assumes it is just interpreted locally by the Logitech firmware. But apparently on the K400+, it is sending a modified escape code to Raspbian, which trigger a mysterious action.