Family HDHP coverage is when the policy covers the taxpayer and at least one other person (even if that person is not eligible to contribute to an HSA).
As for the question of your Medicare coverage, this does not affect your spouse's annual HSA contribution limit at all, unless your spouse chooses to go from Family HDHP coverage to Single HDHP coverage.
She would still be able to contribute to her HSA, it's just that with Single coverage, her annual contribution limit would be reduced.
You going on Medicare otherwise does not affect her HSA at all, only yours (if you had one).
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