Fix leaked anyio streams in streamable_http

[aabmass]

Motivation and Context

Fixes a resource leak. I was seeing this in tests I am writing for a different issue (#421 (comment)). Before:

 | Traceback (most recent call last):
| File ".venv/lib/python3.13/site-packages/anyio/streams/memory.py", line 183, in __del__
| warnings.warn(
| ~~~~~~~~~~~~~^
| f"Unclosed <{self.__class__.__name__} at {id(self):x}>",
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| ...<2 lines>...
| source=self,
| ^^^^^^^^^^^^
| )
| ^
| ResourceWarning: Unclosed <MemoryObjectReceiveStream at 7fbd5bf10a50>

How Has This Been Tested?

Added a new test as first commit in this PR which fails. It passes with the fix, and I was able to remove a bunch of pragma: no cover statements.

Breaking Changes

No

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

Additional context

[Kludex]

Why does the reader moves to the finally but not the writer?

[aabmass]

On L569 it gets stored

# Store writer reference so close_sse_stream() can close itself._sse_stream_writers[request_id] =sse_stream_writer

Should I be closing it here too, or does it need to outlive this function?

[Kludex]

Why this moves up?

[aabmass]

This stays in the except block same as before. Should this happen in finally regardless of exception?

The merge-base changed after approval.

[aabmass]

Tests are fixed now

[Kludex]

We can bump sse-starlette btw, can you do it, please?

[aabmass]

That works for me. Done and removed this fixture

[Kludex]

Thanks @aabmass