refactor: align backend layout and supabase infra

Consolidate backend modules/tests under the backend package while syncing Supabase compose/env config and related plans.

backend/src/v1/auth/router.py

@@ -0,0 +1,49 @@
+from __future__ import annotations
+
+from fastapi import APIRouter, Depends, Response
+
+from v1.auth.dependencies import get_auth_service
+from v1.auth.models import (
+    AuthTokenResponse,
+    LoginRequest,
+    LogoutRequest,
+    RefreshRequest,
+    SignupRequest,
+)
+from v1.auth.service import AuthService
+
+
+router = APIRouter(prefix="/auth", tags=["auth"])
+
+
+@router.post("/signup", response_model=AuthTokenResponse)
+async def signup(
+    payload: SignupRequest,
+    service: AuthService = Depends(get_auth_service),
+) -> AuthTokenResponse:
+    return await service.signup(payload)
+
+
+@router.post("/login", response_model=AuthTokenResponse)
+async def login(
+    payload: LoginRequest,
+    service: AuthService = Depends(get_auth_service),
+) -> AuthTokenResponse:
+    return await service.login(payload)
+
+
+@router.post("/refresh", response_model=AuthTokenResponse)
+async def refresh(
+    payload: RefreshRequest,
+    service: AuthService = Depends(get_auth_service),
+) -> AuthTokenResponse:
+    return await service.refresh(payload)
+
+
+@router.post("/logout", status_code=204)
+async def logout(
+    payload: LogoutRequest,
+    service: AuthService = Depends(get_auth_service),
+) -> Response:
+    await service.logout(payload.refresh_token)
+    return Response(status_code=204)