ci: add web job to workflow to ensure they build (#295)

Author: russellwheatley

.github/workflows/e2e.yml

@@ -225,3 +225,25 @@ jobs:
       - name: "E2E Tests"
         working-directory: tests
         run: flutter test ./integration_test/firebase_ui_test.dart -d macos --dart-define=CI=true
+  web:
+    runs-on: ubuntu-latest
+    timeout-minutes: 15
+    steps:
+      - uses: actions/checkout@b4ffde65f46336ab88eb53be808477a3936bae11
+      - uses: subosito/flutter-action@2783a3f08e1baf891508463f8c6653c258246225
+        with:
+          channel: 'stable'
+          cache: true
+      - uses: bluefireteam/melos-action@720a109b686f61979b4f9f0d14f582ab1637647e
+        with:
+          melos-version: "3.0.1"
+      - name: 'Build Test Applications'
+        run: |
+          cd packages/firebase_ui_auth/example
+          flutter build web
+          cd ../../firebase_ui_database/example
+          flutter build web
+          cd ../../firebase_ui_firestore/example
+          flutter build web
+          cd ../../firebase_ui_storage/example
+          flutter build web