Yes, you are covered by Medicare even if you only have Part A. You cannot have a HSA, not even one contributed by your employer.

You can have an existing HSA, you just are not permitted to contribute, nor is anyone or any employer permitted to contribute, to your HSA for any month that you are covered by Medicare, including Medicare Part A.  You can keep existing funds in the HSA as long as you like.

Presumably have an existing HSA, otherwise you wouldn't be in the HSA section.  Mark "Medicare or None" for each month that you were covered by Medicare Part A.