feat: add LiteLLM as AI gateway provider

[RheagalFire]

Summary

• Adds LiteLLM as a new AI provider, enabling users to route AI requests through 100+ LLM providers (OpenAI, Anthropic, Azure, Bedrock, Vertex AI, Groq, Ollama, etc.) via a single LiteLLM proxy.
• Reuses the existing customApiKey and aiBaseUrl config fields, so no DB migration needed.

Motivation

LiteLLM acts as a unified AI gateway. Instead of configuring individual provider API keys, users can point srcbook at a single LiteLLM proxy that handles provider routing, load balancing, cost tracking, and fallbacks across 100+ providers. Useful for teams that already run a centralized LiteLLM proxy, or users who need providers not directly supported (e.g., AWS Bedrock, Vertex AI).

Changes

• packages/shared/src/ai.mts - added LiteLLM: 'litellm' to AiProvider enum and gpt-4o-mini as default model
• packages/api/ai/config.mts - added case 'litellm': that uses createOpenAI with proxy URL (default http://localhost:4000/v1), reuses customApiKey and aiBaseUrl fields
• packages/web/src/routes/settings.tsx - added LiteLLM option to provider dropdown, added LiteLLM config panel with proxy URL + API key inputs and link to LiteLLM docs

Tests

Live E2E - AI SDK with LiteLLM proxy routing to Claude Sonnet 4.6:

$ node --input-type=module -e '...'

Model: claude-sonnet-4-6
Content: OK
Usage: {"promptTokens":13,"completionTokens":4,"totalTokens":17}
Finish reason: stop

This proves the full chain: createOpenAI (same SDK srcbook uses) -> LiteLLM proxy -> Claude Sonnet 4.6 -> response parsed.

Unit tests (6/6 pass):

$ bunx vitest run test/litellm-provider.test.mts

✓ test/litellm-provider.test.mts  (6 tests) 2ms
Test Files  1 passed (1)
Tests  6 passed (6)

Tests cover: provider enum registration, default model, provider validation, existing providers not broken, invalid provider rejection.

Regression (11/11 pass, 1 pre-existing failure in srcmd.test.mts unrelated to this PR):

$ bunx vitest run

✓ test/tsserver.test.mts  (3 tests)
✓ test/streaming-xml-parser.test.mts  (2 tests)
✓ test/litellm-provider.test.mts  (6 tests)
Tests  11 passed (11)

Risk / Compatibility

• Additive only. Existing providers completely untouched.
• No new dependencies added - uses the existing @ai-sdk/openai package.
• No DB migration needed - reuses customApiKey and aiBaseUrl config fields.
• Default proxy URL is http://localhost:4000/v1 (standard LiteLLM proxy port).

Example usage

In Settings, select "litellm" from the provider dropdown, then:

1. Enter your LiteLLM proxy URL (e.g., http://localhost:4000/v1)
2. Enter your LiteLLM API key
3. Set model to any LiteLLM model ID (e.g., anthropic/claude-3-5-sonnet, openai/gpt-4o, bedrock/anthropic.claude-3-sonnet)

[RheagalFire]

cc @nichochar