feat(saju-lab): main.py + routers (saju 6 + compat 5) + route tests

Phase 2 백엔드 마지막 task — FastAPI app · 11 endpoint · 10 route tests.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

saju-lab/app/main.py

@@ -0,0 +1,33 @@
+"""saju-lab FastAPI app."""
+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+
+from .config import CORS_ALLOW_ORIGINS
+from .routers import saju, compat
+from . import db as db_module
+
+
+app = FastAPI(title="saju-lab")
+
+_origins = [o.strip() for o in CORS_ALLOW_ORIGINS.split(",") if o.strip()]
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=_origins,
+    allow_credentials=False,
+    allow_methods=["GET", "POST", "PATCH", "DELETE", "OPTIONS"],
+    allow_headers=["Content-Type"],
+)
+
+
+@app.on_event("startup")
+def _init():
+    db_module.init_db()
+
+
+@app.get("/health")
+def health():
+    return {"ok": True}
+
+
+app.include_router(saju.router)
+app.include_router(compat.router)