fix: prevent chainlit sub app to default all endpoints

[willydouhard]

Fixing #1819

[dokterbob]

It's a good start but I think we need a more rigorous solution: we should not have to refer to root_path or such things anywhere in our code, but rather move to use of request.url_for(). That way our code becomes less error prone and less sensitive to (the many) edge cases in HTTP routing.

References:

• https://fastapi.tiangolo.com/advanced/templates/?h=url_for#template-context-values
• https://fastapi.tiangolo.com/reference/request/?h=url_for#fastapi.Request.url_for

Regression unit tests

In addition, I would like to request we start writing unit tests for this -- I think https://github.com/Chainlit/chainlit/blob/main/backend/tests/test_server.py is the place.

I'm not 100% sure it's required but we could programmatically spin up a uvicorn. If we do, we can run uvicorn programmatically, e.g. in a pytest fixture using yield for teardown. Make sure to use a random port and check for availability.