Form IRS Pub 969: "Family HDHP coverage is HDHP coverage for an eligible individual and at least one other individual (whether or not that individual is an eligible individual)." That means that you are to indicate that you have family coverage.
It's not clear why TurboTax would indicate that you have an excess contribution if you indicated that you had a family HDHP the entire year (or at least in December), you contributed $7,300 or less for 2022 and you did not indicate any contributions by your spouse (if filing jointly). If you were not covered for December 2022, your contribution limit would be less.
