app-server: structure and test JSON shutdown logs

[bolinfest]

Why

LOG_FORMAT=json and RUST_LOG are supported by app-server, but the behavior was only covered indirectly. We should verify the actual JSONL written by both user-facing entry points: codex app-server and the standalone codex-app-server binary.

The existing processor shutdown message also always said the channel closed, even though the processor can exit for several different reasons. Structured fields make that event more accurate and useful to log consumers.

What changed

• Record the processor exit_reason, remaining connection count, and forced-shutdown state as structured tracing fields.
• Add a shared process-test helper that enables JSON logging, validates every stderr line as JSON, and verifies the top-level timestamp is RFC 3339.
• Cover both codex app-server and codex-app-server, asserting the stable level, fields, and target payload.

Test plan

• just test -p codex-app-server standalone_app_server_emits_json_info_events
• just test -p codex-cli app_server_emits_json_info_events