Correct. But be careful with contributions and when you are no longer eligible. If you contribute under the last month rule (see Pub 969 I believe) and you switch the next year your previous contributions under that rule will be deemed ineligible.
“Presumably you can keep the HSA open and investing?”
Yes.
“Can you still withdraw the funds tax free for health care expenses, even if you now have a more traditional health plan that is not HSA eligible?“
Yes. You can pay for old qualifying expenses, as long as they occurred after you funded the HSA. Or new qualifying expenses.
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