Fix prod startup: add start.sh for backend, fix documents proxy base route

- backend/Dockerfile: run migrations via start.sh before uvicorn instead
  of launching uvicorn directly (prod was skipping Alembic)
- backend/scripts/start.sh: alembic upgrade head + uvicorn exec
- documents_proxy.py: add explicit "" route so GET /api/documents (no
  trailing slash) returns 200 instead of 307 redirect
- README.md: update Containers table, volumes section, and Current State
  to reflect the new 4-container architecture with doc-service

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/Dockerfile

@@ -24,9 +24,11 @@ COPY --from=builder /install /usr/local
 COPY --chown=appuser:appuser app ./app
 COPY --chown=appuser:appuser alembic ./alembic
 COPY --chown=appuser:appuser alembic.ini .
+COPY --chown=appuser:appuser scripts ./scripts
+RUN chmod +x scripts/start.sh
 
 USER appuser
 
 EXPOSE 8000
 
-CMD ["uvicorn", "app.main:app", "--host", "0.0.0.0", "--port", "8000"]
+CMD ["sh", "scripts/start.sh"]

backend/app/routers/documents_proxy.py

@@ -46,11 +46,12 @@ def _forward_headers(request: Request, user_id: str) -> dict:
     return headers
 
 
+@router.api_route("", methods=["GET", "POST"])
 @router.api_route("/{path:path}", methods=["GET", "POST", "PUT", "PATCH", "DELETE"])
 async def proxy_documents(
-    path: str,
     request: Request,
     current_user: User = Depends(get_current_user),
+    path: str = "",
 ) -> StreamingResponse:
     url = f"/documents/{path}" if path else "/documents"
     headers = _forward_headers(request, str(current_user.id))

backend/scripts/start.sh

@@ -0,0 +1,8 @@
+#!/bin/sh
+set -e
+
+echo "[start] running migrations..."
+alembic upgrade head
+
+echo "[start] starting uvicorn..."
+exec uvicorn app.main:app --host 0.0.0.0 --port 8000