feat(slice-1): FastAPI factory + /healthz; self-migrate at startup (INV-1/§6.4)

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

backend/app/platform/deps.py

@@ -0,0 +1,18 @@
+"""FastAPI dependencies — per-request wiring (SD-0001 §6.2 platform/deps).
+
+Yields a pooled connection per request. The pool lives on app.state, built once in
+create_app(). Later slices add the current-session and mailer dependencies here.
+"""
+from __future__ import annotations
+
+from collections.abc import Iterator
+
+import psycopg
+from fastapi import Request
+
+
+def get_conn(request: Request) -> Iterator[psycopg.Connection]:
+    """A pooled connection for the duration of one request."""
+    pool = request.app.state.pool
+    with pool.connection() as conn:
+        yield conn