[Feat] Add OpenAI-compatible inference provider option

[roomote-roomote]

Opened on behalf of Matt Rubens. View the task or mention @roomote-roomote for follow-up asks.

Related issue

Fixes #560

Linked work items

Closes #560

Why this PR exists

• A maintainer explicitly invited this PR in the linked issue or discussion
• I am a maintainer / this is internal Roomote work

What changed

Adds a first-class OpenAI-compatible inference provider so operators can connect any OpenAI API endpoint (LiteLLM proxy, local server, custom gateway, etc.) without guessing between LiteLLM, Ollama, or vLLM.

• Setup catalog entry using OPENAI_COMPATIBLE_BASE_URL and optional OPENAI_COMPATIBLE_API_KEY
• Model discovery and qualification via the shared /v1/models + /v1/chat/completions path
• Inference gateway routing and worker OpenCode @ai-sdk/openai-compatible config
• Public docs page and env-var reference
• Worker configs no longer fall back generic OpenAI-compatible endpoints to OPENAI_API_KEY / OPENAI_BASE_URL

Existing LiteLLM, Ollama, and vLLM providers stay as dedicated named options.

How it was tested

• pnpm --filter @roomote/types exec vitest run for provider catalog and gateway tests
• pnpm --filter @roomote/web exec vitest run for local provider discovery and provider setup fixtures
• pnpm --filter @roomote/worker exec vitest run for OpenCode provider config, including keyless openai-compatible isolation and gateway rebase
• Typecheck on @roomote/types, @roomote/web, and @roomote/worker
• pnpm --filter @roomote/docs check
• Pre-push suite on push

Screenshots

Checklist

• The PR title follows the repo convention: [Fix], [Feat], [Improve], [Refactor], [Docs], or [Chore] followed by a user-facing description
• This PR is small and scoped to one change
• pnpm lint and pnpm check-types pass locally
• I added tests or included a clear manual validation note above
• I removed secrets, tokens, private keys, and customer data from code, logs, and screenshots
• If this change should appear in the changelog, I ran pnpm changeset

[roomote-roomote]

No new code issues found. See task

• apps/worker/src/run-task/agent-home.ts:725-737 The new openai-compatible provider falls back to OPENAI_API_KEY when its optional key is blank, sending that unrelated credential to the configured arbitrary endpoint. Setup qualification omits this header, so a keyless endpoint that rejects bearer auth can pass setup but fail every task; use only OPENAI_COMPATIBLE_API_KEY or no header for this provider.

_{Reviewed a1e53ee}

[mrubens]

@roomote-roomote address the feedback and fix tests

[roomote-roomote]

I'm on it. I routed this request into the existing PR task so follow-up work stays on one Roomote thread for this PR, and I'll keep updates here. See task

[roomote-roomote]

Fixed the review feedback and CI fixture failure in a1e53ee.

• openai-compatible now uses only OPENAI_COMPATIBLE_API_KEY (or no API key); it no longer falls back to OPENAI_API_KEY / OPENAI_BASE_URL
• Added worker coverage for keyless isolation and gateway rebase
• Updated the provider-setup fixture for OPENAI_COMPATIBLE_BASE_URL