## Why
Code-mode callbacks can outlive their initial request and run in separate tasks,
so their trace context must be preserved explicitly.
## What changed
- Preserve the execution context for code-mode callbacks and add spans for
nested tool invocations in the runtime and dispatch broker.
- Propagate each tool invocation span as the parent of its streamed gRPC
callback, falling back to the outer execution context when needed.
- Add a `codex.exec_server.process` span for each process lifetime, including
its process ID and completion result, without retaining the request span.
GitOrigin-RevId: a6059e34d895416f5517e51dad6ca0078355adca
## What changed
- Move the V8 implementation into a dedicated `codex-code-mode-runtime` crate used by `codex-code-mode-host`, removing the embedded runtime fallback from the Codex process.
- Resolve the host executable from the active installation layout and check its availability before selecting tools.
- Fall back to direct tools with a one-time warning when optional code mode is unavailable. Keep `code_mode_only` and `disable_in_process_fallback` configurations fail-closed.
## Testing
- Cover host discovery for standalone and package layouts, including missing hosts and symlinks.
- Verify direct-tool fallback, one-time warnings, and fail-closed code-mode-only behavior.
GitOrigin-RevId: 5aa3c6f1db148b2231fc24089a2ee0e2b00dbddb
