You can’t contribute to an HSA unless you are enrolled in a qualifying high deductible health plan (HDHP( and have no other medical coverage. Medical coverage through the VA, or Medicaid, or Medicare will disqualify you from being able to contribute to an HSA.
If you already have money in an HSA from prior qualified contributions, you can continue to own that HSA account and spend the money on out-of-pocket medical costs even if you are not eligible to make new contributions.