I know it's slightly off topic but is there any chance of getting this to work with Ungoogled Chromium? I thought it would work the same as Edge but alas it does not.
The 1Password app will only connect to trusted browsers that have been whitelisted, and Ungoogled Chromium is unfortunately not in that list. However, since 1Password X works a bit differently in that it doesn't have to connect to the desktop app, it might work in that browser. Have you given that a try already?