Edit -Sorry, I'm not 100% sure if my previous answer was correct as per the
Global Entry for citizens of the UK page does state the following:
Travel Requirements:
All UK Global Entry members must have a valid passport and Electronic System for Travel Authorization (ESTA) or a valid visa. Global Entry members who are not U.S. citizens or U.S. lawful permanent residents must maintain updated visa information with CBP. If a Global Entry member obtains a new visa, or obtains a new petition for a work visa, the member must notify CBP in-person at a Global Entry enrollment center. A member must visit an enrollment center to have CBP add visa and/or update visa information. If the visa information is incomplete or not properly updated with CBP, the Global Entry kiosk may incorrectly calculate the member’s Class of admission and admission date. A member must visit an enrollment center in-person to add or update visa information.
Though you not travelling to the US for the interview, so it's not 100% clear?
There is no where within the Global Entry system to either enter or update ESTA details. There's only sections you can update are your passport and driving licence details if and when they both expire.
In the ESTA application process, it does ask you for your KTN (Known Traveller Number) which is also your Global Entry membership number if you have one but other than that I believe they are separate.
I believe having Global Entry does expedite an ESTA application somewhat though.