add session pinning to llm_chat handler and rewrite session pinning demo

- extend brightstaff llm_chat_inner to extract X-Session-Id, check the
  session cache before routing, and cache the result afterward — same
  pattern as routing_service.rs
- replace old urllib-based demo with a real FastAPI research agent that
  runs 3 independent tool-calling tasks with alternating intents so
  Plano routes to different models; demo.py is a pure httpx client that
  shows the routing trace side-by-side with and without session pinning

demos/llm_routing/session_pinning/demo.sh

@@ -3,9 +3,17 @@ set -e
 
 SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd)"
 export PLANO_URL="${PLANO_URL:-http://localhost:12000}"
+export AGENT_PORT="${AGENT_PORT:-8000}"
+export AGENT_URL="http://localhost:$AGENT_PORT"
 
-echo "Running session pinning demo..."
-echo "PLANO_URL=$PLANO_URL"
-echo ""
+cleanup() {
+    [ -n "$AGENT_PID" ] && kill "$AGENT_PID" 2>/dev/null
+}
+trap cleanup EXIT INT TERM
 
-python3 "$SCRIPT_DIR/demo.py"
+# Start the agent in the background
+"$SCRIPT_DIR/start_agents.sh" &
+AGENT_PID=$!
+
+# Run the demo client
+uv run "$SCRIPT_DIR/demo.py"