The remix chain isn’t very helpful because it is either one of the following projects or a combination of them:
https://api.glitch.com/v1/projects/by/id?id=b952187a-ea2e-4a1c-9055-f455c996a381
https://api.glitch.com/v1/projects/by/id?id=0a59806f-5c0d-468e-84bb-fa5b54ecf500
https://api.glitch.com/v1/projects/by/id?id=929980a8-32fc-4ae7-a66f-dddb3ae4912c
To get the remix chain of the project using the API, you need to refer to project using its ID.