If you entered the HDHP coverage correctly (Family in the early months and Self-only later on, as appropriate), then if TurboTax says that you had excess contributions, then you probably did. The calculations for the annual HSA contribution limit and the consequent excess contributions calculation are arcane and obscure. You can find this by looking at page 6 and 7 in the instructions for form 8889, as well as reviewing the HSA chapters in IRS Pub 969.
Do you have the dollars in the HSA to withdraw the excess? This would be the simplest and most straightforward solution.
Otherwise note that the 6% penalty is 6% of the smaller of the carryover or the amount in your HSA at the end of the year (12-31-2023). So it might not be such a bite.
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