Build and deploy a FastAPI backend with a real database

Build and deploy a FastAPI backend for a small internal API that a separate frontend team's app will call to look up and update shipment tracking records, ending with it actually live at a real, reachable URL — not just runnable inside the Replit workspace.

API SURFACE
Endpoints: GET /shipments/{id}, GET /shipments (paginated, filterable by status), POST /shipments, PATCH /shipments/{id}/status. Every request and response body gets a Pydantic model — no raw dict passed straight through from a request to a database call and back; the model is what gives me actual validation errors instead of a 500 when a client sends a malformed field.

DATA LAYER
Use Replit's managed Postgres database for persistence, with the connection string read from a Replit Secret, never hardcoded in the code even for a "just testing" first pass — a hardcoded connection string committed once tends to stay committed. Write the actual schema (as SQLAlchemy models or raw SQL migrations, your call, but pick one and be consistent) rather than creating tables ad hoc from application code paths that happen to run first — I want a single, explicit place that defines the schema.

RELIABILITY AND HEALTH
Add a /healthz endpoint that checks the actual database connection (not just returning a static 200) and returns a non-200 status if the database is unreachable — this is what a deployment platform's health check should actually be pinging, not the root route. Handle the obvious failure modes explicitly: a request for a resource that doesn't exist returns 404 with a clear message, a validation failure returns 422 with the specific field that failed, and an unexpected exception is caught by a global exception handler that logs the real error server-side but returns a generic message to the client — never a raw stack trace in a production response.

AUTH
A single static API key checked via an X-API-Key header — no full OAuth needed for this internal service yet.

DEPLOYMENT
Deploy this using Replit's Autoscale (this API has bursty, unpredictable traffic rather than a constant load) deployment, not just leaving it running in the workspace's dev server, which stops the moment I close the browser tab. Set up the environment variables/secrets needed for the deployed version specifically, since Replit's deployment environment does not automatically inherit whatever you typed into the workspace's dev-only shell session. After deploying, give me the real, live URL and the exact curl command to hit /healthz and confirm it's actually up, not just that the deploy step reported success.

DOCUMENTATION
Since this is an API with no UI, generate the OpenAPI docs FastAPI provides automatically at /docs, and confirm they're reachable at the deployed URL too, not only in the dev workspace — a common gap is deployment config that works for the app's main routes but accidentally blocks or misconfigures the docs route.

CONSTRAINTS
Add a basic per-API-key rate limit of 100 requests/minute — the frontend team will be given a single shared key for now. Type every function signature — no bare dict or Any where a Pydantic model or a concrete type should be used instead.