Add Codex Desktop App support to thv llm setup

[jerm-dro]

Why

#5783 tracks LLM gateway support for the Codex CLI. Codex also ships a separate Desktop app (Electron, macOS/Windows only — no Linux) for supervising multiple agent threads. It's a distinct install/detection target from the CLI, so it needs its own client entry to be auto-detected and configured by thv llm setup, even though it largely shares config with the CLI.

What we know

Codex Desktop reads the same ~/.codex/config.toml and ~/.codex/auth.json as Codex CLI — same custom model_providers config, same cached login. This is unlike Claude Desktop, which needed a dedicated credential-helper mode (pkg/client ModeCredentialHelper) because it uses a completely separate configLibrary document model.

Practically, this likely means:

• Once Add Codex CLI support to thv llm setup #5783 lands (CLI direct-mode config.toml patching), Codex Desktop may work automatically since it reads the same file — this issue is partly about verifying that, not building a second write path.
• Detection still needs its own client entry (distinct LLMDetectRelPath/binary check for the Desktop app bundle, since "is Codex Desktop installed" is a different check than "is the codex CLI binary on PATH").

Known upstream caveats to account for

• Codex Desktop mixes local custom provider base_url with remote auth.json API key (openai/codex#24457) — when a local custom provider and a remote workspace are both configured, the Desktop app can send the wrong Authorization header. Worth a doc warning if we ship this before OpenAI fixes it.
• No UI in Codex Desktop to change the model for a custom provider mid-session — the model is fixed at session creation.
• macOS/Windows only — Linux users only get this via Codex CLI.

References

• Codex Authentication docs
• Codex Advanced Configuration