Are you willing to get the Covid vaccine when offered?
"Double-vaxxed" = Completion of the first two doses of an mRNA vaccine.
People might call that "fully vaccinated", but these days I think "fully vaccinated" is ambiguous. "Vaccinated" alone is also ambiguous.
Now that I think about it ... I guess the term "boosted" logically dictates that the first two shots took place (assuming it's not a J&J person).