When I launched the App from Spotlight, it told me to move it to the Applications folder even though it's already there.
When I opened the app inside the folder manually, I saw the process pop up in Activity Monitor and disappear again.
Since I needed the App for work I quickly reinstalled it and don't know which exact version caused the issue. I'm also not sure how I could figure out which version it was without the app starting
1Password Version: 8.?
Extension Version: -
OS Version: macOS 12.0.1