Close stdio input before waiting for server exit

[luisangelrod]

Summary

• close the child process's standard input before waiting for stdio server shutdown
• allow well-behaved servers that exit on EOF to complete graceful cleanup without consuming ShutdownTimeout
• add a regression test that verifies disposal observes a clean server exit before half of the configured timeout

Validation

• dotnet test tests/ModelContextProtocol.Tests/ModelContextProtocol.Tests.csproj --filter FullyQualifiedName~StdioClientTransportTests — 54 passed on each of net472, net8.0, net9.0, and net10.0 (216 total)
• dotnet build -c Release — succeeded with 0 warnings and 0 errors
• the new regression test was verified to fail against the previous implementation after approximately 4.1 seconds and pass with this change in approximately 1 second

The full test suite was also attempted locally. Unrelated environment dependencies involving the missing Node conformance helper and a localhost OAuth development certificate prevented a clean full-suite completion. One parallel task-cancellation test also failed during that run and passed when rerun in isolation.

Fixes #1836

Note

This pull request description and implementation were prepared with AI assistance.