a remote worker isn't necessarily an online worker. Remote means the business is established in country A, and the worker works in country B C or D. Possibly you could have applied as a freelancer, I don't know the specifics of your business and the documents and registration you provided them.
extensions are only available in country, typically when you have 30 days or less left on your current permission to stay stamp. Basically you go to the immigration office serving where you're staying at that time, you'll only need your passport, 1900 baht, and to be sure a TM30 has been filed wherever you are staying.