feat: add litellm provider

[RheagalFire]

📝 Pull Request Summary

Add LiteLLM as a first-class AI gateway provider with both native SDK and HTTP proxy support, enabling access to 100+ LLM providers via pip install memu-py[litellm].

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✅ What does this PR do?

• Adds a new LiteLLMSDKClient that uses litellm.acompletion() and litellm.aembedding() directly (no proxy server needed)
• Adds a LiteLLMBackend for users who prefer the HTTP proxy path (client_backend="httpx")
• Registers litellm as a new client_backend option alongside sdk, httpx, and lazyllm_backend
• Adds litellm>=1.80.0,<1.87.0 as an optional dependency
• Adds provider defaults: base_url=http://localhost:4000, api_key=LITELLM_API_KEY, auto-selects litellm client backend
• 11 unit tests covering backend, settings, and SDK client behavior

New files:

• src/memu/llm/litellm_sdk.py - SDK client with drop_params=True for cross-provider compatibility
• src/memu/llm/backends/litellm.py - HTTP proxy backend (inherits OpenAILLMBackend)
• tests/llm/test_litellm_provider.py - 11 unit tests

Modified files:

• src/memu/app/service.py - registered litellm client backend
• src/memu/app/settings.py - provider defaults
• src/memu/llm/backends/__init__.py - registered export
• src/memu/llm/http_client.py - registered in LLM_BACKENDS and embedding backends
• pyproject.toml - optional dependency

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🤔 Why is this change needed?

LiteLLM provides a unified Python SDK for 100+ LLM providers (Anthropic, Azure, Bedrock, Vertex, Groq, Ollama, etc.). Adding it as a native client backend lets users access any supported provider without running a proxy or waiting for per-provider backends to be added.

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🔍 Type of Change

• Bug fix
• New feature
• Documentation update
• Refactor / cleanup
• Other (please explain)

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✅ PR Quality Checklist

• PR title follows the conventional format (feat:, fix:, docs:)
• Changes are limited in scope and easy to review
• Documentation updated where applicable
• No breaking changes (or clearly documented)
• Related issues or discussions linked

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📌 Optional

Live E2E (LiteLLM SDK, no proxy, Azure AI Foundry -> Claude Sonnet):

=== LiteLLM SDK E2E (no proxy) ===
Chat model: azure_ai/claude-sonnet-4-6

--- Chat test ---
Response: 4
Model: claude-sonnet-4-6
Tokens: prompt=20, completion=5

--- Summarize test ---
Summary: LiteLLM is an open-source AI gateway that offers a single, unified
interface for accessing and interacting with over 100 different large language
model (LLM) providers.
Tokens: prompt=44, completion=43

Unit tests (11/11 pass):

TestLiteLLMBackend::test_backend_endpoint PASSED
TestLiteLLMBackend::test_backend_name PASSED
TestLiteLLMBackend::test_backend_payload_parsing PASSED
TestLiteLLMBackend::test_backend_summary_payload PASSED
TestLiteLLMBackend::test_backend_vision_payload PASSED
TestLiteLLMSettings::test_defaults PASSED
TestLiteLLMSettings::test_httpx_backend_preserved PASSED
TestLiteLLMSettings::test_preserves_custom_values PASSED
TestLiteLLMSDKClient::test_chat_calls_acompletion PASSED
TestLiteLLMSDKClient::test_chat_omits_api_key_when_none PASSED
TestLiteLLMSDKClient::test_embed_calls_aembedding PASSED

Lint: ruff check + ruff format --check - clean.

Example usage

SDK backend (recommended):

from memu.app import MemoryService

service = MemoryService(
    llm_profiles={
        "default": {
            "provider": "litellm",
            # client_backend auto-selects "litellm" SDK
            "chat_model": "anthropic/claude-sonnet-4-6",
            "embed_model": "openai/text-embedding-3-small",
        },
    },
    database_config={"metadata_store": {"provider": "inmemory"}},
)

HTTP proxy backend:

service = MemoryService(
    llm_profiles={
        "default": {
            "provider": "litellm",
            "client_backend": "httpx",
            "base_url": "http://localhost:4000",
            "api_key": "sk-your-litellm-key",
            "chat_model": "anthropic/claude-sonnet-4-6",
            "embed_model": "openai/text-embedding-3-small",
        },
    },
    database_config={"metadata_store": {"provider": "inmemory"}},
)

[RheagalFire]

cc @sairin1202 @evan-ak