It seems pretty obvious that if you have the right to not answer officer's questions in consensual encounters (where you're not suspected of a crime) and arrests (where you're charged with a crime), you should also have the right to remain silent during an investigative detention.
But just because it's obvious doesn't mean it's legally protected.
It turns out that the Supreme Court has declined opportunities to clearly establish the right to remain silent during a Terry stop.
Which means that in some cases, a person can be charged with obstruction if they refuse to answer an officer's questions during a Terry stop. Worse yet, if a court later finds that the officer has violated a person's constitutional rights by arresting them for refusing to answer questions, qualified immunity prevents the victim from being compensated for the injustice, because the right to remain silent during a Terry stop is not considered "clearly established."
Here's a link to a piece titled "Obvious But Not Clear: The Right to Refuse to Cooperate with the Police During a Terry Stop." It was published in the American University Law Review in 2020. Written by a University of Denver law professor and an attorney who graduated from that university, it reviews all of the relevant case law and urges the Supreme Court, other courts, and state legislatures to "clearly define" the right, which would remove qualified-immunity protections for officers who violate that right.
https://digitalcommons.wcl.american.edu/cgi/viewcontent.cgi?...