Add builds to E2E workflow

[hsubox76]

Add steps in E2E smoke test just to see if the app will build with a pretty standard webpack config. This would have caught #7005 . The E2E unit tests are run with karma-typescript and don't use webpack at all so they didn't catch this.

[changeset-bot]

⚠️ No Changeset found

Latest commit: f01c9c8

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[google-oss-bot]

Size Report ¹

Affected Products

No changes between base commit (42fa2a1) and merge commit (334bf48).

Test Logs

• Base (42fa2a1): https://github.com/firebase/firebase-js-sdk/actions/runs/4105220931
• Merge (334bf48): https://github.com/firebase/firebase-js-sdk/actions/runs/4108478559

1. https://storage.googleapis.com/firebase-sdk-metric-reports/ie249xvegi.html

[google-oss-bot]

Size Analysis Report ¹

Affected Products

No changes between base commit (42fa2a1) and merge commit (334bf48).

Test Logs

• Base (42fa2a1): https://github.com/firebase/firebase-js-sdk/actions/runs/4105220931
• Merge (334bf48): https://github.com/firebase/firebase-js-sdk/actions/runs/4108478559

1. https://storage.googleapis.com/firebase-sdk-metric-reports/BEot6uNp6W.html

[dwyfrequency]

LGTM