In gateway mode, async tools (vision_analyze, web_extract, session_search)
deadlock because _run_async() spawns a thread with asyncio.run(), creating
a new event loop, but _get_cached_client() returns an AsyncOpenAI client
bound to a different loop. httpx.AsyncClient cannot work across event loop
boundaries, causing await client.chat.completions.create() to hang forever.
Fix: include the event loop identity in the async client cache key so each
loop gets its own AsyncOpenAI instance. Also fix session_search_tool.py
which had its own broken asyncio.run()-in-thread pattern — now uses the
centralized _run_async() bridge.