Write here, or by link of Embassy. Ask your question directly. I would not be surprised if the certificate has to be apostalised in Philippines. I was married to my wife in Thailand. It is registered at Belgian embassy but not bothered to do at Phil 's one. Let us know what they answer. i really hope you not have to get a red ribbon by DFA, took 4 months to have documents, done there.
this is not totally true. In March 2020 Thailand went in lockdown, and it was impossible to enter the country. In autumn, little by little the country opened up, first with special, expensive visa's , and by December, with normal visa, to get end of that month, the visa exemption again. All then by 15 nights quarantaine.
The last I know it was Philippine airlines and Thai. Before I not know now, some indirect flights were not accepted for COE. You can find some flights of Thai on the Embassy pages too. I also think the Philippine airlines were more frequent.