You're bound by the terms and conditions of the Applecare Agreement of the country in which you bought it, but you can get repair service in some other countries. The link to the Asia-Pacific Applecare+ Agreement for purchases after April 21, 2021 is below. I would recommend that you contact Applecare to get specific answers to your questions to help understand the legal fine points.
Here is a link to a recent thread from a user who bought Applecare in Hong Kong and then needed service in another country. It will give you an idea that sometimes it is complicated.
Small prints brother. Sorry that you got stuck. But various local laws prevent from a lot of things. I think the worldwide support should be there in US, Canada, Europe at least.