Make resolve_dependencies async with dual sync/async factory support

[david-debest]

Parent

#27

What to build

Make the dependency injection resolver async-aware so that Depends factories can be either def or async def.

Resolver: resolve_dependencies() becomes async def. For each Depends factory, detect whether it is a coroutine function via asyncio.iscoroutinefunction(). Async factories are awaited directly; sync factories are called directly (no to_thread — factories are typically fast initializers). Caching semantics are unchanged: cache=True factories are called at most once per invocation, cache=False factories are called fresh each time.

Transitive resolution: The recursive call to resolve a factory's own dependencies must also be awaited, since nested factories may themselves be async.

Overrides: dependency_overrides behavior is unchanged — an override factory replaces the original and may itself be sync or async independently of the original.

Acceptance criteria

• resolve_dependencies() is async def
• Async Depends factories (async def) are detected and awaited
• Sync Depends factories (def) continue to work without changes
• Nested/transitive resolution works when mixing sync and async factories
• dependency_overrides works with async replacement factories
• Caching semantics (cache=True/False) preserved for both sync and async factories
• All DI tests updated to async and passing
• uv run ruff check . passes

Blocked by

• Replace requests with httpx and make ClientProtocol async #28