If you already have a Covid extension 60 days will be added to your current extension of stay. If this is your first Covid extension it will be 60 days from the date of your application. The day the program ends just means the last day someone can apply for this type of extension.
It also depends on the airline. I normally fly Korean from the USA to Bangkok. They are a stickler for the rules. Once my brother and I were being questioned by the check in agent. She kept asking where are return flight was. We were flying on a roundtrip from BKK to LAX to BKK. I told her this flight is the return ticket. When I told her we live in Bangkok she acted like she never heard of such a thing. I showed her my reentry permit and told her this is my permission to reenter Thailand, I am a long term resident and do not need a flight out. It took her a while to grasp the concept but she finally let us board.
Since you are in Bangkok contact Med Park hospital on Rama 4 in Khlong Toei. They are one of the designated hospitals for foreigners to get vaccinated. They even had some Pfizer that was set aside for foreigners only. If you are eligible the vaccination is free. By the way. Thailand is no longer vaccinating with Sinovac. Supplies have run out and they are not ordering any more. The protocol now is AZ first dose and Pfizer or AZ second dose.