Not if the borders are officially closed... Last time I took a flight to BKK (with Lufthansa) from Frankfurt, they definitely requested an "onward flight"... Otherwise, no boarding possible... Fortunately, I had one, so, no problem. Next time, I will do the same. ;-)
"Should" is not enough... Best is to call the airline and ask the requirement to board a flight to BKK... And comply with the requirements... Otherwise, huge stress possible... ;-)
I do my complete heath Check Up at the Christian Hospital. Recommended by the Swiss Embassy. Easy to get to by bus. Not too expensive. Very professional.
Takes 10 minutes. No Cert needed. Just "double" ID (passeport and diving licence for example). If one branch says no, try another one... shop around in touristic places.
First an Extension of 30 days of your "Exemption Stamp" (1'900 THB), then a 3-months "Non-O" visa (1'900 THB) and then a yearly Extension (1'900 THB). Ask your Immigration bureau which documents exactly you need. They know the best...And don't forget the 800k THB on a Thai Bank account...