Is your feature request related to a problem? Please describe.
The Burr UI is a FastAPI application.
However the construction of it and its routes aren't amenable to being used as a "sub-app" in another FastAPI application.

Describe the solution you'd like
Create a parameterized function to create the FastAPI application and/or create one that takes an existing FastAPI application and mounts the Burr UI under a certain path.

Describe alternatives you've considered
You can hack around it. But it's not pretty.

Additional context
This would enable you to have serving and tracking in the same FastAPI app!