🧹 [Code Health] Refactor duplicate house invite processing logic

[deitaur]

🎯 What: The code health issue addressed is duplicate logic for processing house joining (inserting memberships, updating invites, adding notifications).
💡 Why: Moving this into a shared helper processInvite improves maintainability as there is only one place to change if the join procedure requires modification in the future.
✅ Verification: I validated the code syntactically with node -c, ensured tests didn't break due to this change specifically, and a code review confirmed the extracted function perfectly matches the prior duplicate implementation while preserving specific error handling.
✨ Result: A cleaner routes/houses.js with zero duplicated database query sequences.

---

PR created automatically by Jules for task 827109158679317306 started by @deitaur

[google-labs-jules]

👋 Jules, reporting for duty! I'm here to lend a hand with this pull request.

When you start a review, I'll add a 👀 emoji to each comment to let you know I've read it. I'll focus on feedback directed at me and will do my best to stay out of conversations between you and other bots or reviewers to keep the noise down.

I'll push a commit with your requested changes shortly after. Please note there might be a delay between these steps, but rest assured I'm on the job!

For more direct control, you can switch me to Reactive Mode. When this mode is on, I will only act on comments where you specifically mention me with @jules. You can find this option in the Pull Request section of your global Jules UI settings. You can always switch back!

New to Jules? Learn more at jules.google/docs.

---

For security, I will only act on instructions from the user who triggered this task.