feat(opencode): add LiteLLM provider integration

[RheagalFire]

Issue for this PR

Closes #29935

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

Adds LiteLLM as a built-in provider. Sets LITELLM_BASE_URL (and optionally LITELLM_API_KEY) to connect. Models are auto-discovered from the proxy's /v1/models endpoint at
startup, no manual config needed.

Since LiteLLM is a gateway (not a fixed provider), it's not in models.dev. The provider auto-seeds into the database when env vars are detected.

Files changed:

• provider.ts: Custom loader with env var resolution, database seeding, and /v1/models discovery
• schema.ts: Well-known litellm provider ID
• sprite.svg / types.ts: Provider icon
• en.ts / settings-providers.tsx / dialog-select-provider.tsx: UI strings and notes

Env var	Description
LITELLM_BASE_URL	Base URL of the LiteLLM proxy (e.g. http://localhost:4000)
LITELLM_API_KEY	API key / master key for the proxy (optional if proxy has no auth)

Related: #29308, #6231, #14468

How did you verify your code works?

1. Started LiteLLM proxy backed by Azure AI Foundry with claude-sonnet-4-6 and claude-opus-4-7
2. Set LITELLM_BASE_URL + LITELLM_API_KEY env vars
3. Ran TUI (bun dev), LiteLLM models auto-discovered and appear in model picker
4. Sent messages, streaming works
5. Tested tool calling (file listing), works through the proxy
6. Switched between models (sonnet/opus), works
7. Ran web UI (bun dev serve + bun run --cwd packages/app dev), provider visible in settings, chat works
8. Tested disconnect/reconnect flow

Screenshots / recordings

ceb2-3aa7-47fd-b86f-e27af97bfe24-2.mp4

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

[github-actions]

The following comment was made by an LLM, it may be inaccurate:

Potential Duplicate/Related PRs Found:

1. PR feat(opencode): add LiteLLM provider with auto model discovery #14468 - feat(opencode): add LiteLLM provider with auto model discovery

   • feat(opencode): add LiteLLM provider with auto model discovery #14468
   • Why related: This appears to be an earlier or alternative implementation of LiteLLM provider integration with auto model discovery. Current PR feat(opencode): add LiteLLM provider integration #29937 is likely updating/completing this feature (PR feat(opencode): add LiteLLM provider with auto model discovery #14468 is mentioned in the "Related" section).

2. PR fix: inject cache_control on content blocks for openai-compatible proxies to Anthropic backends (Bifrost, LiteLLM, Databricks) #25985 - fix: inject cache_control on content blocks for openai-compatible proxies to Anthropic backends (Bifrost, LiteLLM, Databricks)

   • fix: inject cache_control on content blocks for openai-compatible proxies to Anthropic backends (Bifrost, LiteLLM, Databricks) #25985
   • Why related: Involves LiteLLM proxy handling and OpenAI-compatible protocol features that may be relevant to the integration.

3. PR feat(opencode): add LLM provider fallback chain #26292 - feat(opencode): add LLM provider fallback chain

   • feat(opencode): add LLM provider fallback chain #26292
   • Why related: Provider integration feature that may have overlapping scope with adding a new gateway provider.

The most significant is PR #14468 - verify if it's the predecessor/duplicate of the current work or if it's a separate issue being addressed by PR #29937.