bug: httpx.AsyncClient created per-request in server-https/app.py

Context

server-https/app.py (line 202) creates a new httpx.AsyncClient on every incoming request rather than reusing a shared instance.

Problem

Every request opens a new connection pool and tears it down — redundant TLS handshakes, file descriptor churn, no benefit from HTTP keep-alive. Under any real load this becomes measurable overhead and can exhaust fd limits.

Why This Order

Same file as the CORS fix (#76) and replacing the linear query flow in server-https/app.py. Fix the client lifecycle first so subsequent changes don't build on top of the broken pattern.

Acceptance Criteria

• A single httpx.AsyncClient is created at app startup via FastAPI lifespan
• All route handlers reuse it via request.app.state
• Client is properly closed on shutdown — no ResourceWarning in tests

Related

• server-https/app.py:202
• Parent tracking issue: #72
• Blocks: Kagent agent layer and replacing the linear query flow in server-https/app.py

Start in server-https/app.py at line 202 and trace how the FastAPI application and route handlers access the HTTP client. Move client creation into the app lifespan and make handlers reuse the shared instance through request.app.state. Done means one client is created at startup, closed on shutdown, and tests produce no ResourceWarning.