fix: drain accepted JSON-RPC requests after read EOF

[matthewchen94]

Fixes #2678.

This changes the JSON-RPC dispatcher shutdown path so read EOF does not immediately cancel request handlers that were already accepted. The dispatcher now:

• marks the connection closed and wakes outbound waiters after read EOF,
• keeps the write stream open briefly for accepted inbound requests to finish their response writes,
• bounds that drain window to avoid hanging shutdown,
• tracks active inbound requests through the response write window, not just while they are present in _in_flight.

This targets stdio servers driven with redirected stdin, where EOF can arrive immediately after the last JSON-RPC request is read while an async tool call is still mid-await. In that case the response should be flushed to stdout before shutdown.

Validation:

• python3 -m py_compile src/mcp/shared/jsonrpc_dispatcher.py tests/shared/test_jsonrpc_dispatcher.py passed on the patched files.
• Added a dispatcher-level regression test that accepts a request, closes the read side, and asserts the response is still written.

[cubic-dev-ai]

1 issue found across 2 files

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[matthewchen94]

Updated this PR to address the review and failed CI:\n\n- Scoped EOF draining behind an explicit dispatcher opt-in so default transport-close semantics still cancel in-flight handlers immediately.\n- Enabled that opt-in only for stdio read streams, where redirected stdin can EOF after the final accepted request while stdout still needs to flush the response.\n- Tracked the transport_builder rejection path in the drain counter, so spawned INTERNAL_ERROR responses are not cancelled before reaching the peer.\n- Merged latest main and added regression coverage for both accepted handler responses and builder-rejection responses.\n\nAll CI checks are green on f4a8fc9.