Add turn-start MCP and connector availability analytics

[mzeng-openai]

Summary

• extend codex_turn_event with the generic MCP server names and connector identities exposed at turn start
• derive the snapshot from the first frozen, post-policy direct/deferred MCP exposure
• sort, deduplicate, and cap both fields while excluding schemas, descriptions, URLs, and full tool metadata
• add analytics serialization/reducer coverage plus focused core and app-server turn tests

Why

The connector-runtime RFC calls for distinguishing inventory availability from actual usage. Turn analytics currently reports MCP tool-call counts, so a zero cannot tell us whether no MCP/connector tools were available or whether available tools simply were not called.

RFC: https://app.notion.com/p/3818e50b62b081d28e88f9c3342d4d10

Payload

codex_turn_event now includes:

• turn_start_available_mcp_server_names
• turn_start_available_mcp_server_names_truncated
• turn_start_available_connectors as { connector_id, connector_name }
• turn_start_available_connectors_truncated

Each identity list is stably ordered, deduplicated, capped at 100 items and 16 KiB of serialized JSON, and accompanied by a truncation flag. The codex_apps MCP server is represented through connector identities rather than as a generic server name.

The snapshot represents post-policy exposure: model visibility, connector accessibility, app policy, and direct/deferred search gating have been applied. It intentionally precedes final router schema validation, tool-name collision resolution, and code-mode exclusions.

Validation

• just test -p codex-analytics — 86 passed
• just test -p codex-core defers_apps_and_non_app_mcp_tools
• just test -p codex-app-server --test all turn_start_tracks_thread_originator_in_analytics
• just fix -p codex-analytics
• just fix -p codex-core
• just fix -p codex-app-server
• just fmt
• release app-server test-target compilation

Draft status

Draft pending final cleanup around cumulative byte-budget test coverage and a few small reducer/test simplifications identified in the final review.