Fix completed request cancellation cleanup

[FU-max-boop]

Summary

Fixes #2610.

• Suppress the cancellation raised by CancelScope.__exit__ only after a RequestResponder has completed and sent its response.
• Keep cancellation propagation unchanged for incomplete responders.
• Add focused regression coverage for the completed and incomplete cleanup paths.

The implementation is rebased onto the maintained v1.x line (v1.29.0), where BaseSession and this cleanup path remain active.

Validation

• pytest tests/shared/test_session.py tests/server/test_cancel_handling.py -q — 11 passed
• ruff format --check src/mcp/shared/session.py tests/shared/test_session.py
• ruff check src/mcp/shared/session.py tests/shared/test_session.py
• pyright --pythonpath .venv/bin/python src/mcp/shared/session.py tests/shared/test_session.py
• git diff --check

[FU-max-boop]

CI note: I inspected the two failed Ubuntu jobs. They fail in existing tests that are not changed by this PR: tests/interaction/lowlevel/test_timeouts.py::test_session_level_timeout_applies_to_every_request timed out during initialize, and tests/shared/test_streamable_http.py::test_client_crash_handled hit an httpx.ConnectError while connecting to the local test server.

Both pass locally on this branch:

uv run --frozen --no-sync pytest tests/interaction/lowlevel/test_timeouts.py::test_session_level_timeout_applies_to_every_request -q
uv run --frozen --no-sync pytest tests/shared/test_streamable_http.py::test_client_crash_handled -q

I do not have permission to rerun Actions on this repository, but these look like transient CI timing/port failures. Happy to patch if they reproduce consistently.

[FU-max-boop]

Rebased this fix onto v1.29.0 / v1.x and retargeted the PR because main is now v2 and no longer contains this BaseSession path. The PR is back to one commit and two files. Local validation passes: 11 focused session/cancellation tests, Ruff, Pyright, and git diff --check.

[maxisbey]

Thanks for the PR, and sorry it sat here without a proper review.

We're closing most of the open PR backlog. v2 is out and changed a lot of the SDK, so many older PRs no longer apply as written, and we're a small team that realistically doesn't have the capacity to work through the rest.

If this still matters to you on v2, the most useful thing you can do is open an issue (or comment on the existing one) with your use case and a repro. Hearing why it matters to you is what we use to decide what to prioritise.

_{AI Disclaimer}