Add backend testing pipeline

[kyleburgess2025]

No description provided.

[sentry]

🔍 Existing Issues For Review

Your pull request is modifying functions with the following pre-existing issues:

📄 File: backend/src/main.ts

Function	Unhandled Issue
moodLog	TypeError: Cannot read properties of undefined (reading 'user_id') ... Event Count: 1 Affected Users: 0

---

_{Did you find this useful? React with a 👍 or 👎}

[github-actions]

Visit the preview URL for this PR (updated for commit 1be04f3):

• https://getbaselineapp--pr449-burgess-pipeline-p4tf7mrj.web.app
• https://baseline-links--pr449-burgess-pipeline-5t0ylw0q.web.app
• https://baseline-api--pr449-burgess-pipeline-9ixt29y0.web.app

_{(expires Tue, 02 Sep 2025 03:04:12 GMT)}

_{🔥 via Firebase Hosting GitHub Action 🌎}

_{Sign: ab0c34a7eb1b98345b28ddf98e64e1d623b28ac1}