feat(providers): add Auxen as a declarative provider

[ai-auxen]

Adds Auxen as a declarative provider in goose. Auxen hosts per-customer dedicated LLM endpoints (Llama 3.1/3.2, Qwen 2.5, Mistral, Gemma 2, Mixtral, Phi-3, Command R) with an OpenAI-compatible `/v1/chat/completions` API. Each instance is a dedicated GPU billed per-minute of runtime — no token charges, no monthly minimums.

Why declarative

Auxen instances are OpenAI-wire-compatible, so this follows the same pattern as the existing `atomic_chat.json` declarative provider — uses `${AUXEN_API_BASE}` env-var interpolation in `base_url` because every Auxen instance has its own per-instance URL of the form `https://api.auxen.ai/v1/inst_xxx/v1\` issued by the Auxen dashboard. Users set both `AUXEN_API_BASE` and `AUXEN_API_KEY` (the `auxk_*` token) when configuring the provider.

Files

• `crates/goose/src/providers/declarative/auxen.json` (new) — declarative provider with the 12 catalog models and per-instance env-var binding
• `documentation/docs/getting-started/providers.md` — row in the Available Providers table (alphabetical, between Atomic Chat and Avian)

Companion PRs (Auxen distribution series)

• BerriAI/litellm#28532 — LiteLLM provider
• vercel/ai#15536 — Vercel AI SDK community provider
• langchain-ai/docs#4146 — LangChain docs (Python + JS)
• run-llama/llama_index#21764 — LlamaIndex Python
• continuedev/continue#12473 — Continue.dev provider
• cline/cline#10988 — Cline OpenAI-compatible quickstart
• crewAIInc/crewAI#5911 — CrewAI provider config
• pydantic/pydantic-ai#5586 — Pydantic AI docs
• Helicone/helicone#5685 — Helicone gateway
• langfuse/langfuse-docs#2990 — Langfuse provider page
• npm: `@auxen/ai-sdk-provider` (live)

AI agent (Claude) assisted in drafting this PR.

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[chatgpt-codex-connector]

Remove duplicated AUXEN_API_KEY config field

Defining AUXEN_API_KEY in both api_key_env and env_vars creates two config entries for the same key, because declarative registration always adds api_key_env first and then appends every env_vars entry without deduplication (crates/goose/src/providers/provider_registry.rs). In setup/config UIs this yields duplicate required secret fields for Auxen, which is confusing and can cause inconsistent form handling when clients assume keys are unique.

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