With the Mac app

Same sign-in, same Pro, same snippet format, and three different relationships to what the Mac keeps in iCloud, because a browser cannot sync on its own:

• Notes go both ways, through the folder. Point the extension at the Mac app's notes folder in iCloud Drive (it is in the file browser's sidebar under iCloud Drive, then TypeFire) and both apps read and write the same files; iCloud carries the changes between your Macs. An edit here is on the Mac the next time it looks, and the other way round.
• Clips come one way. Connect the Mac's clips folder (Settings → Clips, Pro) and the clips the Mac syncs show up here, pictures included, read only. What you copy in the browser stays in the browser.
• Snippets do not sync. The library lives in this browser. To move snippets, Export Package for Browser Extension on one side and Import Browser Extension on the other, in either direction. Both installed on one Mac, an abbreviation expands once.