Logitech Wave keyboard pairing issues after Tahoe update on iMac

I have an iMac running on Tahoe 26.0.1. When this was installed and updating, I now have issues pairing my Logitech Wave keyboard with the Mac after I shut it down. When I restart the Mac, I have to put in another keyboard that isn't bluetooth to get to my home screen.

Another annoying thing that has happened today is that when I press the keys F11 or F12 to increase/decrease the volume, I get a random screen appear to the right of the screen with what looks like code on it when I press F12, and on F11 the screen disappears.

I can still operate the volume by pressing fn and then F11 or F12, but before I installed Tahoe I could do it straight by pressing the key F11 or F12 without fn too.

Any advice greatly appreciated.

[Re-Titled by Moderator]

Original Title: Logitech keyboard pairing issues