feat: add user model and registration endpoint

backend/app/routes/auth.py

@@ -0,0 +1,27 @@
+from fastapi import APIRouter, Depends, HTTPException, status
+from sqlalchemy import select
+from sqlalchemy.ext.asyncio import AsyncSession
+
+from app.db import get_db
+from app.models.user import User
+from app.schemas import RegisterRequest, UserOut
+from app.security import hash_password
+
+router = APIRouter(prefix="/auth", tags=["auth"])
+
+
+@router.post("/register", response_model=UserOut, status_code=status.HTTP_201_CREATED)
+async def register(payload: RegisterRequest, db: AsyncSession = Depends(get_db)):
+    existing = await db.scalar(select(User).where(User.username == payload.username))
+    if existing is not None:
+        raise HTTPException(status_code=status.HTTP_409_CONFLICT, detail="username taken")
+
+    user = User(
+        username=payload.username,
+        password_hash=hash_password(payload.password),
+        email=payload.email,
+    )
+    db.add(user)
+    await db.commit()
+    await db.refresh(user)
+    return user