Does Medicare count as a High Deductible Health Plan (HDHP)?
No. Neither Medicare Part A nor Medicare Part B count as an HDHP. This means that if you enroll in Medicare, you can't contribute to your HSA with pre-tax dollars.
When you enroll in Medicare, your HSA overseer should change your HSA contributions to $0 per month.
Your HDHP coverage when you start Medicare would be None.
However, even though you can't make new pre-tax contributions to your HSA after enrolling in Medicare, you can still use HSA funds to pay for medical expenses.