Now I do believe there could be a fee for your ins co.
Just hunt around. Maybe it was free because I'm 77.
On a related note, when I signed up online for the covid vaccine there was a page for insurance information. If you checked “medicare”, all the rest of the page was grayed out. The only personal information they asked for was first, middle initial, last, address, mother’s maiden name, date of birth. No ss #, no driver’s license #, only email address and phone where you could be reached.