It seems the extension is using outdated URLs (https://keep.google.com/keep instead of https://keep.google.com/).
Uninstall the current extension. Then, try my modified version. Download the zip file, extract it, goto the URL opera://extensions in Opera GX, turn on developer mode, click "load unpacked" and point it to the "0.1.0_0" folder where manifest.json is at. That will install it. Then, click the cube icon on the address bar and pin the extension's icon.
I didn't test the whole extension. I just tested that it gives you the sign on page now. Let me know how it works.
See the forum thread for the extension as others are having the problem too. If your testing of my fixed version turns out okay, I'll link to it there for others.