Link to extension's page in the Chrome web store so we're all talking about the exact same extension?

Is the extension supposed to work all by itself or does it require that F-Secure Total or F-Secure ID Protection is installed where the extension just communicates with the F-Secure program's password manager?

I assume the latter. Which one do you have installed?

There's an old thread about F-Secure that implies that the F-Secure extension doesn't work in Opera and that this is not new. The extension probably requires the use of the nativeMessaging Chromium extensions API. If so, it's often the case that the program/extension is only set up to only allow nativeMessaging with specific browsers where Opera isn't one of them. If that's the case for F-Secure. F-Secure has to be fixed to allow Opera to communication with it from the extension installed in Opera.