Track app server startup analytics by transport

[anp-oai]

Why

We want visibility into app-server startup latency so regressions can be detected across both standalone app-server launches and the embedded app-server runtime used by the TUI.

What Changed

• Added a codex_app_server_started analytics event with:
  • rpc_transport to identify the startup path (stdio, websocket, or in_process)
  • duration_ms for measured startup duration
  • created_at and runtime metadata
• Emitted the startup event from:
  • standalone app-server startup
  • embedded in-process app-server startup used by the TUI
• Updated existing analytics integration helpers and assertions to handle the startup event being emitted before later lifecycle events.
• Documented the startup event timestamp and duration fields.

Validation

• Added integration coverage for standalone startup reporting rpc_transport: "stdio".
• Added integration coverage for embedded startup reporting rpc_transport: "in_process".

[anp-oai]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Nice work!

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