test(02-01): add failing tests for AUTH-01 through AUTH-04 and install shadcn Alert

- Install shadcn Alert component (alert.tsx)
- LoginPage.test.tsx: 4 test cases for gradient bg, wordmark, Alert error, SVG icon
- RegisterPage.test.tsx: 2 test cases for gradient bg, wordmark
- All tests fail as expected (features not yet implemented)

frontend/src/components/ui/alert.tsx

@@ -0,0 +1,76 @@
+import * as React from "react"
+import { cva, type VariantProps } from "class-variance-authority"
+
+import { cn } from "@/lib/utils"
+
+const alertVariants = cva(
+  "group/alert relative grid w-full gap-0.5 rounded-lg border px-2.5 py-2 text-left text-sm has-data-[slot=alert-action]:relative has-data-[slot=alert-action]:pr-18 has-[>svg]:grid-cols-[auto_1fr] has-[>svg]:gap-x-2 *:[svg]:row-span-2 *:[svg]:translate-y-0.5 *:[svg]:text-current *:[svg:not([class*='size-'])]:size-4",
+  {
+    variants: {
+      variant: {
+        default: "bg-card text-card-foreground",
+        destructive:
+          "bg-card text-destructive *:data-[slot=alert-description]:text-destructive/90 *:[svg]:text-current",
+      },
+    },
+    defaultVariants: {
+      variant: "default",
+    },
+  }
+)
+
+function Alert({
+  className,
+  variant,
+  ...props
+}: React.ComponentProps<"div"> & VariantProps<typeof alertVariants>) {
+  return (
+    <div
+      data-slot="alert"
+      role="alert"
+      className={cn(alertVariants({ variant }), className)}
+      {...props}
+    />
+  )
+}
+
+function AlertTitle({ className, ...props }: React.ComponentProps<"div">) {
+  return (
+    <div
+      data-slot="alert-title"
+      className={cn(
+        "font-medium group-has-[>svg]/alert:col-start-2 [&_a]:underline [&_a]:underline-offset-3 [&_a]:hover:text-foreground",
+        className
+      )}
+      {...props}
+    />
+  )
+}
+
+function AlertDescription({
+  className,
+  ...props
+}: React.ComponentProps<"div">) {
+  return (
+    <div
+      data-slot="alert-description"
+      className={cn(
+        "text-sm text-balance text-muted-foreground md:text-pretty [&_a]:underline [&_a]:underline-offset-3 [&_a]:hover:text-foreground [&_p:not(:last-child)]:mb-4",
+        className
+      )}
+      {...props}
+    />
+  )
+}
+
+function AlertAction({ className, ...props }: React.ComponentProps<"div">) {
+  return (
+    <div
+      data-slot="alert-action"
+      className={cn("absolute top-2 right-2", className)}
+      {...props}
+    />
+  )
+}
+
+export { Alert, AlertTitle, AlertDescription, AlertAction }

frontend/src/pages/LoginPage.test.tsx

@@ -0,0 +1,65 @@
+import { render, screen, act } from '@testing-library/react'
+import { describe, it, expect, vi } from 'vitest'
+import { LoginPage } from './LoginPage'
+
+vi.mock('react-i18next', () => ({
+  useTranslation: () => ({ t: (key: string) => key }),
+}))
+
+const mockAuth = {
+  user: null,
+  loading: false,
+  login: vi.fn(),
+  register: vi.fn(),
+  logout: vi.fn(),
+  token: null,
+  refetch: vi.fn(),
+}
+
+describe('LoginPage branding', () => {
+  it('AUTH-01: wrapper div has a linear-gradient background', () => {
+    const { container } = render(
+      <LoginPage auth={mockAuth} onToggle={vi.fn()} />
+    )
+    const wrapper = container.firstElementChild as HTMLElement
+    expect(wrapper?.style.background).toContain('linear-gradient')
+  })
+
+  it('AUTH-02: renders a wordmark element with a gradient background style', () => {
+    render(<LoginPage auth={mockAuth} onToggle={vi.fn()} />)
+    const wordmark = screen.getByTestId('wordmark')
+    expect(wordmark).toBeTruthy()
+    expect(wordmark.style.background).toBeTruthy()
+  })
+
+  it('AUTH-04: renders role="alert" when an error is present', async () => {
+    const failingLogin = vi.fn().mockRejectedValue(new Error('Invalid credentials'))
+    const authWithError = { ...mockAuth, login: failingLogin }
+
+    render(<LoginPage auth={authWithError} onToggle={vi.fn()} />)
+
+    const form = document.querySelector('form')!
+    await act(async () => {
+      form.dispatchEvent(new Event('submit', { bubbles: true, cancelable: true }))
+    })
+
+    const alertEl = await screen.findByRole('alert')
+    expect(alertEl).toBeTruthy()
+  })
+
+  it('AUTH-04: the alert contains an SVG icon (AlertCircle)', async () => {
+    const failingLogin = vi.fn().mockRejectedValue(new Error('Invalid credentials'))
+    const authWithError = { ...mockAuth, login: failingLogin }
+
+    render(<LoginPage auth={authWithError} onToggle={vi.fn()} />)
+
+    const form = document.querySelector('form')!
+    await act(async () => {
+      form.dispatchEvent(new Event('submit', { bubbles: true, cancelable: true }))
+    })
+
+    const alertEl = await screen.findByRole('alert')
+    const svgEl = alertEl.querySelector('svg')
+    expect(svgEl).toBeTruthy()
+  })
+})

frontend/src/pages/RegisterPage.test.tsx

@@ -0,0 +1,33 @@
+import { render, screen } from '@testing-library/react'
+import { describe, it, expect, vi } from 'vitest'
+import { RegisterPage } from './RegisterPage'
+
+vi.mock('react-i18next', () => ({
+  useTranslation: () => ({ t: (key: string) => key }),
+}))
+
+const mockAuth = {
+  user: null,
+  loading: false,
+  login: vi.fn(),
+  register: vi.fn(),
+  logout: vi.fn(),
+  token: null,
+  refetch: vi.fn(),
+}
+
+describe('RegisterPage branding', () => {
+  it('AUTH-03: wrapper div has a linear-gradient background', () => {
+    const { container } = render(
+      <RegisterPage auth={mockAuth} onToggle={vi.fn()} />
+    )
+    const wrapper = container.firstElementChild as HTMLElement
+    expect(wrapper?.style.background).toContain('linear-gradient')
+  })
+
+  it('AUTH-03: renders a wordmark element with data-testid="wordmark"', () => {
+    render(<RegisterPage auth={mockAuth} onToggle={vi.fn()} />)
+    const wordmark = screen.getByTestId('wordmark')
+    expect(wordmark).toBeTruthy()
+  })
+})