Why

This is stacked on #24800. After exposing CodexConfig, the remaining SDK naming still referred to the underlying transport through error and client class names. The SDK-facing vocabulary should center on Codex itself.

What changed

• Renamed exported exceptions to CodexError and CodexRpcError.
• Renamed internal transport wrappers to CodexClient and AsyncCodexClient, and removed the private AppServerTurn alias in favor of Turn.
• Updated high-level docs and docstrings to say Codex or Codex protocol where users interact with the SDK, while retaining precise executable and transport references where those details matter.

API impact

from openai_codex import CodexError, CodexRpcError

AppServerError and AppServerRpcError are no longer exported.

Validation

• uv run --frozen --extra dev ruff check src/openai_codex scripts examples tests
• Tests are deferred to online CI for this PR.