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/stores/auth.ts

@@ -1,27 +1,18 @@
-import { create } from 'zustand'
-import { persist } from 'zustand/middleware'
-import type { User } from '../types/api.ts'
-
-interface AuthState {
-  user: User | null
-  token: string | null
-  isAuthenticated: boolean
-  setAuth: (user: User, token: string) => void
-  logout: () => void
-}
-
-export const useAuthStore = create<AuthState>()(
-  persist(
-    (set) => ({
-      user: null,
-      token: null,
-      isAuthenticated: false,
-      setAuth: (user, token) => set({ user, token, isAuthenticated: true }),
-      logout: () => set({ user: null, token: null, isAuthenticated: false }),
-    }),
-    {
-      name: 'cartsnitch-auth',
-      partialize: (state) => ({ user: state.user, isAuthenticated: state.isAuthenticated }),
-    },
-  ),
-)
+import { create } from 'zustand'
+
+/**
+ * Minimal auth state for UI reactivity.
+ *
+ * Session management is handled by Better-Auth via httpOnly cookies.
+ * This store only tracks whether we have an active session for UI
+ * gating (protected routes, nav state). No tokens in memory or localStorage.
+ */
+interface AuthState {
+  isAuthenticated: boolean
+  setAuthenticated: (value: boolean) => void
+}
+
+export const useAuthStore = create<AuthState>()((set) => ({
+  isAuthenticated: false,
+  setAuthenticated: (value) => set({ isAuthenticated: value }),
+}))