If you apply in your home country for a non-immigrant visa, you are applying for an OA visa.  To get an OA visa you must show proof of health insurance that covers COVID.  It would be a good idea to maintain the insurance you now have, assuming your insurance provides coverage in Thailand.

If arrive on a tourist visa then convert that to a non-immigrant visa in Thailand, there is no proof of insurance required for the 12 month extensions.  However, you will need to show proof of insurance as part of your entry requirements, but that can be short term travel insurance.

Note: If you arrive on a Tourist visa you will need the same coverage on travel insurance for the duration of your visa.