Feat/litellm provider (#12823)

* feat: add LiteLLM provider types, env var, credentials, and auth choice

Add litellm-api-key auth choice, LITELLM_API_KEY env var mapping,
setLitellmApiKey() credential storage, and LITELLM_DEFAULT_MODEL_REF.

* feat: add LiteLLM onboarding handler and provider config

Add applyLitellmProviderConfig which properly registers
models.providers.litellm with baseUrl, api type, and model definitions.
This fixes the critical bug from PR #6488 where the provider entry was
never created, causing model resolution to fail at runtime.

* docs: add LiteLLM provider documentation

Add setup guide covering onboarding, manual config, virtual keys,
model routing, and usage tracking. Link from provider index.

* docs: add LiteLLM to sidebar navigation in docs.json

Add providers/litellm to both English and Chinese provider page lists
so the docs page appears in the sidebar navigation.

* test: add LiteLLM non-interactive onboarding test

Wire up litellmApiKey flag inference and auth-choice handler for the
non-interactive onboarding path, and add an integration test covering
profile, model default, and credential storage.

* fix: register --litellm-api-key CLI flag and add preferred provider mapping

Wire up the missing Commander CLI option, action handler mapping, and
help text for --litellm-api-key. Add litellm-api-key to the preferred
provider map for consistency with other providers.

* fix: remove zh-CN sidebar entry for litellm (no localized page yet)

* style: format buildLitellmModelDefinition return type

* fix(onboarding): harden LiteLLM provider setup (#12823)

* refactor(onboarding): keep auth-choice provider dispatcher under size limit

---------

Co-authored-by: Peter Steinberger <steipete@gmail.com>

docs/providers/index.md

@@ -39,6 +39,7 @@ See [Venice AI](/providers/venice).
 - [Anthropic (API + Claude Code CLI)](/providers/anthropic)
 - [Qwen (OAuth)](/providers/qwen)
 - [OpenRouter](/providers/openrouter)
+- [LiteLLM (unified gateway)](/providers/litellm)
 - [Vercel AI Gateway](/providers/vercel-ai-gateway)
 - [Together AI](/providers/together)
 - [Cloudflare AI Gateway](/providers/cloudflare-ai-gateway)