Drain stdio responses after redirected stdin EOF

[Asti1982]

Fixes #2678.

Summary

• keep the stdio write side open after redirected stdin EOF so already accepted request handlers can finish and flush responses
• bound stdio EOF draining with a 5s timeout while preserving the existing immediate-cancel behavior for other transport closes
• add a regression test that drives an MCPServer through redirected stdin and asserts response ids 0, 1, and 2 are all written before process exit

Tests

• python -m ruff check src/mcp/shared/session.py src/mcp/server/session.py src/mcp/server/lowlevel/server.py src/mcp/server/mcpserver/server.py tests/issues/test_2678_stdio_eof_drain.py
• python -m ruff format --check src/mcp/shared/session.py src/mcp/server/session.py src/mcp/server/lowlevel/server.py src/mcp/server/mcpserver/server.py tests/issues/test_2678_stdio_eof_drain.py
• python -m pyright src/mcp/shared/session.py src/mcp/server/session.py src/mcp/server/lowlevel/server.py src/mcp/server/mcpserver/server.py tests/issues/test_2678_stdio_eof_drain.py
• python -m pytest tests/issues/test_2678_stdio_eof_drain.py tests/server/test_cancel_handling.py tests/server/test_session.py -q

[StantonMatt]

I checked this against the stdio EOF case from #2678.

The focused tests pass locally:

TMPDIR=.codex-tmp/tmp UV_CACHE_DIR=.codex-tmp/uv-cache uv run --frozen pytest tests/issues/test_2678_stdio_eof_drain.py tests/server/test_cancel_handling.py tests/server/test_session.py -q

I also ran a local memory-stream probe for the shutdown edge where an accepted tools/call handler never finishes after stdin/read EOF. With drain_in_flight_on_read_eof=True and drain_in_flight_on_read_eof_timeout_seconds=0.2, server.run() returned after the bounded drain window instead of hanging indefinitely.

That covers the main lifecycle risk I was looking for: redirected stdin gets a chance to flush accepted responses, but EOF is still a bounded shutdown signal. I did not find an issue in this pass.

[Kludex]

You've opened a duplicated pull request, please search opened PRs before creating new ones. Duplicated from #2680.