While doing login to some online resource press your configured key combination (by default it's Ctrl+B, ⌘+B). OtpExt icon will turn green.
A request to launch OTP manager app should appear. Agree to launch your OTP app.
In your OTP manager: copy your one-time password into clipboard (this depends on the specifics of a partucular OTP app)
Back to browser:
paste just copied password to appropriate form field or
double click in any place of your login form holding Ctrl key or
press your configured Key combination to do the same
Now you can disable OtpExt by pressing first key combination (default Ctrl+B, ⌘+B). OtpExt icon will turn red.
To be done...