At last! Thanks for helping me to fix this very annoying issue, @dubhead, @m4ssacre, and @albertchong! For anyone just encountering this thread who doesn't speak German, here is a complete explanation of the workaround in English with screenshots.
First, open System Preferences --> Security and Privacy, and make sure that Logitech Options is allowed to modify accessibility settings:
Second, open Logitech Options, and click on the upper right hand corner to add Opera as an application with its own special settings:
Third, with Opera selected, click on the mouse back button to set the button up:
Fourth, select "Keystroke Assignment" from the left-hand list, click in the right hand window to add the custom keystroke, and then press command (apple key, windows key) and the left arrow:
Fifth, click on the mouse forward button to set the button up:
Sixth (and finally), repeat step four for the forward button, using the command key and the right arrow:
I have to say that having my mouse settings move up into the software layer is irritating, but F*** - software is eating the world, right?