I will try.....
You have installed the Logitech Options software that works with Catalina, yes??
If so, this might be helpful to you.....
but first, there's a firmware update tool for use with 10.14 and Logitech keyboards...
here: (yup, link)
https://support.logi.com/hc/en-ca/articles/360035037273-Firmware-Update-Tool
and here's some Catalina and/or Mojave stuff...... *yup, 'nother link....*
https://support.logi.com/hc/en-ca/articles/360023203954-Logitech-Options-permission-prompts-on-macOS-Catalina-and-macOS-Mojave
your keyboard should be connected via USB-C, though bluetooth is an option.....Should appear under system preferences....keyboards....... you might have to do a "Set Up new Keyboard" as well, dumb, maybe, simple, perhaps, but.....
and it does mention that the latest version of Logitech Options (8.02 or later) is officially compatible with Catalina.
Hmmmm.... I always thought that a keyboard was a keyboard, was a keyboard...in that, you just plugged 'em in, via USB, whatever they were, and they just worked, period. Apparently that's not always the case.....
anyways, good luck and let us know how you made out
john b