1Password classic extension autofills Firefox main window instead of private window

Hey @nekno ,

Indeed, having both extensions enabled simultaneously will cause some unwanted side effects. When you try to open and fill from Classic, it will send a command to the desktop app, at which point the desktop app will try to contact the new extension as it takes priority. I recommend you disable one of them at all times. If you want to use both, you can separate them into two different Firefox user profiles: https://support.mozilla.org/en-US/kb/profile-manager-create-and-remove-firefox-profiles

Is enabling the new 1Password extension in private windows on the roadmap (I don't quite understand why it isn't allowed now)?

Extensions can run in private browsing, it is not a feature on the extension's side but on the browser's side.
Simply right click the extension's icon on the top right corner, select "Manage Extension" and change the option there to allow it to run in private browsing mode.