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There are authenticator extensions for web browsers.

Unapproved by the company.

So its their device you are using? otherwise how to they know what authenticator you are using? Most use the same standard.

Except Microsoft Authenticator. That's what my company uses and this is the only reason I ever use my work phone.

Bank has its own Authenticator app. That’s how.

Depends on the technology used - not everything is TOTP.