test: add Vitest and Playwright testing infrastructure

- Add Vitest for unit tests (39 tests)
  - cached-responses.test.ts
  - ai-providers.test.ts
  - chat-helpers.test.ts
  - utils.test.ts
- Add Playwright for E2E tests (3 smoke tests)
  - Homepage load
  - Japanese locale
  - Settings dialog
- Add CI workflow (.github/workflows/test.yml)
- Add vitest.config.mts and playwright.config.ts
- Update .gitignore for test artifacts

.github/workflows/test.yml

@@ -0,0 +1,63 @@
+name: Test
+
+on:
+  pull_request:
+    branches: [main]
+  push:
+    branches: [main]
+
+jobs:
+  lint-and-unit:
+    name: Lint & Unit Tests
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+
+      - name: Setup Node.js
+        uses: actions/setup-node@v4
+        with:
+          node-version: "20"
+          cache: "npm"
+
+      - name: Install dependencies
+        run: npm ci
+
+      - name: Run lint
+        run: npm run check
+
+      - name: Run unit tests
+        run: npm run test -- --run
+
+  e2e:
+    name: E2E Tests
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+
+      - name: Setup Node.js
+        uses: actions/setup-node@v4
+        with:
+          node-version: "20"
+          cache: "npm"
+
+      - name: Install dependencies
+        run: npm ci
+
+      - name: Install Playwright browsers
+        run: npx playwright install chromium --with-deps
+
+      - name: Build app
+        run: npm run build
+
+      - name: Run E2E tests
+        run: npm run test:e2e
+        env:
+          CI: true
+
+      - name: Upload test results
+        uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: playwright-report
+          path: playwright-report/
+          retention-days: 7