I can't find anything that confirms he was under oath. Some articles call it "an interview". Some say "to testify" behind closed doors.
March 2005: Palm Beach police begin investigating Epstein
May 2006: Police officials sign paperwork to charge Epstein with multiple counts of...
July 2006: Epstein is arrested
June 2008: Epstein pleads guilty
May 2009: Virginia Giuffre, files a lawsuit
July 2009: Epstein is released from jail
2010 Gates meets Russian bridge player Mila Antonova
...Through Boris Nikolic, a close Gates adviser, Antonova was introduced to Epstein to help her raise funds for her initiative, which sought to promote bridge
August 2011: Epstein in email, In essence, this will allow Bill to have access to higher quality people, investment, allocation, governance without upsetting either his marriage or the sensitvities of the current foundation employees.
July 18, 2013: Epstein email, "dear bill, I cannot believe that you have chosen to disregard our friendship developed of over the last 6 years." eg since 2007, not "2011"
November 2013: Antonova and Nikolic meet with Epstein at his NYC townhouse
Antonova begins living in an apartment that Epstein provided her.
2017: Epstein emails Gates about Antonova after Gatess extramarital affair ended and asked Gates to reimburse him for Antonovas coding school costs.
https://www.theguardian.com/us-news/2023/may/21/jeffrey-epstein-extort-bill-gates-extramarital-affair
also: https://www.snopes.com/fact-check/epstein-emails-bill-gates-std/