feat: add LiteLLM as custom model provider

[RheagalFire]

Summary

• Adds LiteLLM as a custom model 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.
• Follows the existing custom model pattern (same structure as Ollama, OpenRouter, HuggingFace).

Motivation

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

Changes

• packages/types/src/ai.types.ts - added LiteLLM = 'LiteLLM' to CUSTOM_MODELS enum, added LiteLLM entry to CUSTOM_MODEL_DEFINITIONS with default proxy URL, model docs link, and API key docs link
• packages/icons/src/lib/Icons/LiteLLM.svelte - new icon component (bullet train, matching LiteLLM's brand)
• packages/icons/src/lib/main.ts - registered LiteLLM icon in the icon map and exports

Tests

Live E2E - basic completion via LiteLLM proxy routing to Claude Sonnet 4.6:

=== Test 1: Basic completion ===
Status: 200
Model: claude-sonnet-4-6
Content: OK
Finish: stop

Live E2E - streaming via LiteLLM proxy:

=== Test 2: Streaming ===
Streamed: Hello!

SSE chunks parsed correctly through the same /v1/chat/completions endpoint Surf uses for Ollama and OpenRouter custom models.

Error handling - invalid model:

=== Test 3: Invalid model ===
Status: 200
Error handled: YES

All 3 tests use raw fetch("http://localhost:4000/v1/chat/completions") matching the exact call path Surf uses for custom models via OPEN_AI_PATH_SUFFIX.

Risk / Compatibility

• Additive only. No existing models or providers modified.
• No new dependencies - LiteLLM proxy is OpenAI-compatible, uses the same request/response format as Ollama and OpenRouter.
• 3 files changed, 18 lines added.

Example usage

1. Start a LiteLLM proxy:

pip install litellm
litellm --model anthropic/claude-3-5-sonnet --port 4000

2. In Surf Settings > AI > Custom Model, select "LiteLLM"

3. Enter model name using LiteLLM's provider/model format:

openai/gpt-4o-mini           # OpenAI via LiteLLM
anthropic/claude-3-5-sonnet  # Anthropic via LiteLLM
azure/gpt-4                  # Azure via LiteLLM
bedrock/anthropic.claude-3   # AWS Bedrock via LiteLLM
vertex_ai/gemini-pro         # Vertex AI via LiteLLM
groq/llama-3.3-70b           # Groq via LiteLLM

4. Edit the proxy URL

https://my-proxy.example.com/v1/chat/completions   # remote proxy

5. Enter your LiteLLM proxy API key (if required)

[RheagalFire]

cc @aavshr