Ben, you are confusing Health lnsurance required by OA Visa and Travel(covid) Insurance required for entry in to Thailand.
An O Extension does not require proof of Insurance but to get the Thai Pass you need travel insurance, normally for 1 month, to qualify for the Thai Pass.
whatever you want to call it, you will not be able to go straight to the gate. You will need to go to a check in counter to have your documents checked and your boarding pass printed.