sayyid5416 Al Salaamu 3laykum and thank you for your question.
As you have said, calendar methods are specific to countries (or regions). You can see the list of currently supported methods at https://aladhan.com/islamic-calendar-api#get-/islamicCalendar/methods or if you have a JSON plugin in your browser, just call https://api.aladhan.com/v1/islamicCalendar/methods.
As you will see, currently the 2 supported countries might clearly just be Saudi Arabia (with multiple methods, but this covers all of the GCC except perhaps Oman) and Turkey (but not everyone in Turkey adheres to the Diyanet calendar). The old MATHEMATICAL method is also still there if you wanted to use the older calculation which was adjustable.
All this is coming from a new underlying library - https://github.com/islamic-network/calendar. This library supports both astronomical and mathematical calculation methods, and both can be extended to include the calculation methods of other countries, like Morocco, India, Pakistan, and so on so forth.
But for all these cases, we either need the astronomical data or the mathematical algorithm they use to compute the date, and it can just be added to the library.
If you have access to the data or can help source it, we can add more calendar calculation methods.
I hope this helps answer the question, to some extent, at least.
