Unable to upgrade recent 1Password through App Store in macOS Big Sur 11.2.3 (20D91)

The official support gave me the answer.

  1. Quit all browsers
  2. Open main 1Password window
  3. Press ⌃ + ⌥ + ⌘ + Q to quit and indeed it quits all processes.

Weird that the CLI approach didn't work.

Anyway - solved.