I'm entering HSA information and TurboTax asserts that the HDHP coverage for my wife lapsed for a time in 2024, when it did not. Why is this and how can I correct it?

Take a closer look at the question on the screen just prior to the one telling you there was a lapse in coverage.

If both you and your spouse are covered under the same family plan, then the person with the HDHP in their name will indicate they had a family plan.  The other person will indicate they had None because the HDHP was not in their name.