[codex] Add incremental chat completion traces

[brandonkachen]

Summary

Adds a new chat_completion_traces BigQuery table for efficient coding-agent trace storage from the chat completions endpoint. The endpoint now records a trace row before provider dispatch, storing only appended message deltas after the first snapshot for a trace lineage.

Details

• Adds a non-optional trace_session_id to new client run state and chat completion trace rows.
• Skips writing the new table for old clients that do not send trace_session_id.
• Uses trace_session_id for root-agent conversation lineage and run_id for child-agent lineage isolation.
• Keeps only message hashes in a bounded server-side cache and advances the cache only after a successful BigQuery insert.
• Adds Jest-compatible trace tests and mocks env-validating modules so the web package test runner can load them.

Validation

• bun run --cwd web test --runTestsByPath src/llm-api/__tests__/chat-completion-trace.test.ts
• bun test web/src/app/api/v1/chat/completions/__tests__/completions.test.ts
• bun run --cwd web typecheck
• bun run --cwd common typecheck
• bun run --cwd packages/bigquery typecheck
• bun run --cwd sdk typecheck
• bun run --cwd cli typecheck