As he should have, because it was a witch hunt being performed on a, to my knowledge, innocent man, and they were fishing for anything they could use without having any evidence of wrongdoing. He said in his diary he disliked the president and their behavior. That’s not a crime. And yes, on the matters he received a blanket pardon from actions performed “January 1, 2014, through January 19, 2025, arising from Fauci's service as NIAID Director, Chief Medical Advisor, or member of the White House coronavirus task forces”. If he refused to testify on specifics they can use their congressional powers to compel through their constitutional powers via imprisonment, fines, or both. (Brown v. Walker)
Burdick v. United States Allows fauci to refuse his pardon or pardons and then employ his fifth amendment right. Also if someone being compelled has performed crimes or suspects they have or will be charged for state crimes they may invoke their fifth to protect themselves against that while also accepting a pardon, but they are still protected against federal charges.
If congress had actually been interested in some truth or testimony from fauci to get to the bottom of some events, they could have used under 18 U.S.C. § 6005 via a U.S. District Court order a grant of immunity that would have allowed him to testify while protecting against malicious or resulting state prosecutions, but they offered no such deal, while also having no claims of evidence of impropriety, showing it was a fishing expedition and an attempt to get viral clips for political gain. Which they got by him invoking his fifth, causing morons across the Internet to then claim that proves guilt.