feat(Dockerfile): add root multi-stage Dockerfile for Dokploy

- Stage 1 (node:20): builds Vue.js frontend to /app/dist
- Stage 2 (python:3.12): FastAPI serves API + static files
- main.py: serve Vue.js dist via StaticFiles if /app/dist exists
- Removes GET / route (replaced by frontend index.html)

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

backend/app/main.py

@@ -1,6 +1,9 @@
 """FastAPI application entry point."""
+import os
+
 from fastapi import FastAPI
 from fastapi.middleware.cors import CORSMiddleware
+from fastapi.staticfiles import StaticFiles
 
 from app.api.attachments import router as attachments_router
 from app.api.audit_log import router as audit_log_router
@@ -64,13 +67,13 @@ app.include_router(organizations_admin_router, prefix="/api")
 app.include_router(public_router, prefix="/api")
 
 
-@app.get("/")
-def root() -> dict[str, str]:
-    """Root endpoint."""
-    return {"message": "Space Booking API"}
-
-
 @app.get("/health")
 def health() -> dict[str, str]:
     """Health check endpoint."""
     return {"status": "ok"}
+
+
+# Serve Vue.js frontend in production (when /app/dist exists)
+_dist_dir = os.path.join(os.path.dirname(__file__), "..", "..", "dist")
+if os.path.isdir(_dist_dir):
+    app.mount("/", StaticFiles(directory=_dist_dir, html=True), name="static")