Add default /docs route to list information about the SSE MCP server

[mconflitti-pbc]

Is your feature request related to a problem? Please describe.
Would be useful to have an equivalent to something like how FastAPI generates OpenAPI docs and are automatically accessible at /docs route.

Describe the solution you'd like
Add a /docs route to the starlette app that provides information about the mcp server (available tools, prompts, resources, version, etc.)

Describe alternatives you've considered
none

Additional context
Basic example I currently use:

[panz2018]

I have developed web servers that integrate MCP SSE functionality:

• Using FastAPI: fastapi_mcp_sse
• Using Starlette: starlette_mcp_sse

These servers can be extended with custom routes while retaining full MCP SSE capabilities. For the FastAPI, you can find the OpenAPI docs after starting the server:

• Documentation (Swagger UI): http://localhost:8000/docs
• Documentation (ReDoc): http://localhost:8000/redoc