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/models.py

@@ -0,0 +1,35 @@
+from __future__ import annotations
+
+from pydantic import BaseModel, EmailStr, Field
+
+
+class SignupRequest(BaseModel):
+    email: EmailStr
+    password: str = Field(min_length=6)
+    display_name: str | None = None
+
+
+class LoginRequest(BaseModel):
+    email: EmailStr
+    password: str = Field(min_length=6)
+
+
+class RefreshRequest(BaseModel):
+    refresh_token: str = Field(min_length=1)
+
+
+class LogoutRequest(BaseModel):
+    refresh_token: str = Field(min_length=1)
+
+
+class AuthUser(BaseModel):
+    id: str
+    email: EmailStr
+
+
+class AuthTokenResponse(BaseModel):
+    access_token: str
+    refresh_token: str
+    expires_in: int
+    token_type: str
+    user: AuthUser