Am I approved for a COE if the Thai embassy has requested my passport and a money order?

LA consulate.

I did my visa first...a month before flight.

I applied for my COE about a week before flight.

Then have to do covid test to apply and get f2f 72 hours before flight.

In my case, I sent all my documents' soft copy to embassy first to ask if I am eligible for visa. They told me to send all papers including passport. I did through DHL (as it was from another country). The next day, they call me and asked me for the $40 deposit. One the deposit is done online, immediately they released my passport stamped with visa and a COE letter. For you case, I guess you visa and COE is approved alteady.

Are you in the US? If so then yes, the application for the Visa and COE is together and on the Washington DC embassy page. Its different than what the rest of the world uses. And what you are describing is the process. You fill out all the online stuff and upload the documents. You then get a email to mail in the passport and documents. Once you get the passport back with the visa you will get an email with a link asking to update your COE application. Once that is done you will get the COE approval. Depending on when your flight is they may wait until it is a little closer to your departure date

COE does NOT need a fit-to-fly certificate. You get the FTF within 72hrs of your flight.

The COE is separate from the visa. After you get your passport back, you can apply for the COE. It's online and they email you the COE though, within 24 hours.