Your hotel didn't do the covid test, the hospital did. if you really want the document (which you're entitled to) then you have to ask the hospital. But no, all 3 of my covid tests in the sandbox I never got any paper from.
Non-OA is a 1 year multiple entry visa that requires health insurance and can ONLY be obtained in your home country or country of legal residence.
A Non-O based on retirement is a 90 day single entry visa that can be extended 1 year. It does not require health insurance and can be obtained in most countries and from inside Thailand (transition from a tourist visa or visa exemption). The initial 90 day Non-O requires proof of 800k baht, but the 1 year extension requires 800k baht in a Thai bank account for 60 days before you apply for the extension, and you cannot remove the money for the duration of your stay (you can, but you won't be able to renew the extension).
Unfortunately you need to be on a non immigrant visa to obtain or renew a 5 year license. If you'll be on a tourist visa, you'll revert back to a 2 year temporary license when you renew it.