@forestview
Yes, if you turn 65 in 2025 (not 2024) then your contribution eligibility for 2024 depends on your medical coverage. You indicate that you will leave the group plan in May, so you have 4 months of eligibility ($3100). Whether or not you have additional eligibility depends on what kind of insurance, if any, you maintain for the rest of 2024.
I don't see anything in publication 969 that says that a continuation plan (COBRA coverage after you leave the job) would not qualify, as long as the plan is a qualifying plan. In addition, you are allowed to use your HSA funds to pay the COBRA premiums if you want. If there is a rule that COBRA coverage does not make you eligible to make contributions, I would want to see that in writing some place. If you bought a qualifying marketplace plan to cover you until Medicare started, that would also allow you to make contributions.
