Why has Google Authenticator Chrome extension suddenly lost all accounts? How to recover?

I have been using Google Authenticator Chrome extension for some years, on my Windows and macOS computers. Suddenly it has no accounts in it. I’m pretty sure I saved a backup somewhere, but I can’t find it. (The Windows version was probably 10, and perhaps even 7. The problem happened when I was running the latest version of macos Sequoia. Since then I have done the upgrade to Tahoe.) Authenticator comes from the Chrome web store, https://chromewebstore.google.com/detail/authenticator/bhghoamapcdpbohphigoooaddinpkbai )

Can anyone tell me the format of such backup files, as then I may be able to use grep to scan files and match some pattern that such backups contain.

Or do they have a standard filename extension?

I have searched my computer for filenames containing “auth” and patterns that match yyyymmdd digits, without finding anything promising.