dsh-lcx-codex: Completing Native Compact, Hosted Search, and Prompt Cache for DSH's GPT Responses path

When developing agents using the GPT/OpenAI Responses route in DeepSeek Harness (DSH), if the compression, Replay, and search stages do not align with the provider's native capabilities, issues such as mid-way implementation changes and repeated cache invalidations are easily encountered. DSH's philosophy is "everything is a plugin," and these gaps are perfectly suited to be filled by plugins. The `dsh-lcx-codex` introduced below performs exactly this: it takes over the DSH GPT Responses path to provide Native V2 Compact/Replay, Hosted Search, Prompt Cache, and continuous web operations.