The way that Medicare "backdating" works, is that if you sign up for Medicare at your FRA (Full Retirement Age), there is no backing dating of the Medicare benefits. There is backdating only if you start Medicare after your FRA, and the SSA backdates your coverage to your FRA - but never more than 6 months back.
The SSA says:
For RIB applications filed after FRA, we allow up to 6 months retroactivity. However, for those who file less than 6 months after FRA, we only pay retroactive benefits back to the month of FRA attainment.
RIB - Retirement insurance benefits, i.e., Medicare.
So if your spouse is 70 (i.e., waiting until the maximum Social Security starts) and her FRA is 66 years, 8 months, then the Medicare would be backdated only 6 months (i.e. in part of her 69th year).
You will need to determine her FRA and determine how that relates to the date she started Medicare, to know of there was a look-back or not.
Unfortunately, as Opus noted, no one can make an HSA contribution on another person's behalf if that other person is not an eligible individual. So if that HSA was opened by you then, the $600 is in excess, and you will be invited to withdraw is before April 15, 2025. This is the cheapest and simplest solution.
If your wife actually owned the HSA, then come back and tell us and we will have a different story.
You asked how you would enter all this.
1. In the HSA interview, tell TurboTax that you had Medicare for all twelve months.
2. If your wife does not have an HSA, TurboTax will not ask about her coverage.
3. TurboTax will not ask about your daughter's coverage in any case - that would go on her return.
4. When TurboTax tells you that you have excess contributions (the $600), then be agreeable and say that you will withdraw it (if you have the cash). You will have to contact your HSA custodian and request a "withdrawal of excess contributions" (use this exact phrase, so they will keep their paperwork correct). Note that many HSA custodians have an online form to do this. DO THIS BEFORE APRIL 15th.
5. TurboTax may or may not ask you how you contributed the $600 (that will depend on what you have already told TurboTax). If you contributed the $600 through an employer, then because it was removed from Wages when your W-2 was printed, then the excess is automatically added back to Other Income on your 2024 return. If the $600 was contributed directly to the HSA custodian, then it is just removed from your return as a deduction.
6. Early next year, the HSA custodian will send you a 1099-SA with $600 in box 1, your earnings in box 2, and a distribution code of "2" in box 3. The $600 will be ignored, and the earnings will be added to Other Income on your 2025 return.
7. The $5,000 disbursement (if made in 2024) should already appear on a 1099-SA that you should have received.
Opus did point out that your wife could make a retroactive contribution to her own HSA, which she could open by contributing to it. This also has to be done by April 15th. She could make a contribution to the HSA custodian, specifying that it is for 2024, not 2025.
The amount that she could contribute will depend on what the result of the backdating calculation is. It sounds like she would have one to seven months available for the contribution window. Your wife could contribute up to $5,425 for the 7 months window, if that is what she had. $5,425 = ($8,300 + $1,000) x 7/12.
If she does this, then you will enter that both of you have HSAs in the "Tell us about your health accounts" screen. And TurboTax will also ask about your spouse's HDHP coverage to which she will respond that she had Medicare part of the year.
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