fix: buffer stdio server writes during progress notifications

[2830500285]

Summary

• buffer the server stdio write stream by one message so a handler can queue its final response while stdout is still flushing an earlier notification
• add a regression test covering a slow notification write followed by a response send

Fixes #1141.

Validation

• uv run --frozen --no-sync pytest tests/server/test_stdio.py tests/shared/test_progress_notifications.py -q
• uv run --frozen --no-sync ruff format --check src/mcp/server/stdio.py tests/server/test_stdio.py
• uv run --frozen --no-sync ruff check src/mcp/server/stdio.py tests/server/test_stdio.py
• uv run --frozen --no-sync pyright src/mcp/server/stdio.py tests/server/test_stdio.py

Note: local uv run --frozen sync attempted to fetch the git dependency strict-no-cover, but GitHub fetches for that dependency were failing from this machine. I used the already-synced virtualenv with --no-sync for the targeted checks above.

[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}