Another “Sorry, we can’t check you in online” datapoint for a UK - LHR - USA flight.
FWIW, new passport and new ESTA not previously used to enter the USA.
Checked in without issue at the airport.
BA’s error message “Travel Authorisation for the US can’t be found for the passport details you’ve provided. Please check you have a valid ESTA or provide your US visa number.” is unnecessarily alarmist in these situations.