feat: migrate authentication to Better-Auth (Phase 1)

Replace hand-rolled JWT auth with Better-Auth session-based authentication.

- Scaffold auth/ Node.js service with Better-Auth, bcrypt password compat,
  Postgres adapter mapped to existing users table
- Add Alembic migration (002) creating sessions, accounts, verifications
  tables and migrating password hashes to accounts table
- Update FastAPI auth dependency to validate sessions via shared DB
  (supports both cookie and Bearer token)
- Remove registration/login/refresh endpoints from API gateway (now
  handled by Better-Auth service)
- Update frontend to use better-auth/react client with httpOnly cookies
  (no tokens in localStorage or memory)
- Rewrite auth store, Login, Register, Dashboard, Settings, ProtectedRoute
  to use session-based auth
- Update all tests to create sessions directly in DB instead of JWT tokens

Resolves CAR-27
See plan: CAR-26#document-plan

Co-Authored-By: Paperclip <noreply@paperclip.ing>

src/cartsnitch_api/schemas.py

@@ -6,28 +6,8 @@ from uuid import UUID
 from pydantic import BaseModel, EmailStr, Field
 
 # ---------- Auth ----------
-
-
-class RegisterRequest(BaseModel):
-    email: EmailStr
-    password: str = Field(min_length=8, max_length=128)
-    display_name: str = Field(min_length=1, max_length=100)
-
-
-class LoginRequest(BaseModel):
-    email: EmailStr
-    password: str
-
-
-class RefreshRequest(BaseModel):
-    refresh_token: str
-
-
-class TokenResponse(BaseModel):
-    access_token: str
-    refresh_token: str
-    token_type: str = "bearer"
-    expires_in: int
+# Registration, login, and session management are handled by Better-Auth (auth/ service).
+# These schemas are for the profile management endpoints only.
 
 
 class UpdateUserRequest(BaseModel):