fix: preserve exception propagation through transport cleanup

[jlowin]

When exceptions occur during client initialization (e.g., McpError from server middleware), they were being swallowed and converted to "generator didn't yield" errors. This specifically affected in-memory transport where the server lifespan (including Docket's background worker context managers) is nested inside the client's task group - the complex cleanup chain was suppressing exceptions.

Root cause: anyio task groups suppress exceptions when cancel_scope.cancel() is called during cleanup.

Fix: Capture exceptions before task group cleanup and re-raise them after the task group exits cleanly:

exception_to_raise: BaseException | None = None
async with anyio.create_task_group() as tg:
    try:
        async with ClientSession(...) as session:
            yield session
    except BaseException as e:
        exception_to_raise = e
    finally:
        tg.cancel_scope.cancel()

if exception_to_raise is not None:
    raise exception_to_raise

Also preserves McpError type in _connect() so callers can catch protocol-level errors:

async with Client(server) as client:
    ...
# Now raises McpError instead of RuntimeError wrapping McpError

Relevant to fixing #2531

[coderabbitai]

Walkthrough

The pull request enhances exception handling in the FastMCP client across two files. In client.py, the error handling logic is updated to import and preserve McpError exceptions alongside httpx.HTTPStatusError when session tasks report failures. In transports.py, a new exception capture mechanism is introduced in the connect_session method that catches exceptions during task group execution and re-raises them after cleanup is complete. These changes ensure exceptions are properly propagated to callers rather than being suppressed during task group cancellation.

Pre-merge checks and finishing touches

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 33.33% which is insufficient. The required threshold is 80.00%.	You can run @coderabbitai generate docstrings to improve docstring coverage.

✅ Passed checks (2 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title 'fix: preserve exception propagation through transport cleanup' clearly summarizes the main change: fixing exception propagation in transport cleanup logic.
Description check	✅ Passed	PR description clearly explains the problem, provides code examples, and lists the changes made. All required sections from the template are addressed.

✨ Finishing touches

• 📝 Generate docstrings

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch fix-exception-propagation-in-transport

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