feat: introduce (authenticated) route group layout for auth-protected pages

[aminamos]

Summary:

Resolves #116.
Introduces Next.js (authenticated) route group with shared auth layout and documentation in docs/architecture/authenticated-route-groups.md.

Expected behavior:

Authenticated routes share a unified route group without leaking auth checks into URL paths.

Testing tips:

1. Checkout feat/116-authed-route-groups.
2. Run yarn test.

Please make sure these boxes are checked before submitting your pull request - thanks!

• Run the unit tests with yarn test to make sure you didn't break anything
• Add or update any needed documentation to the repo
• Format the title like "feat: [new feature short description]". Title must follow the Conventional Commit Specification(https://www.conventionalcommits.org/en/v1.0.0/).
• Linked all relevant issues
• Include screenshot(s) showing how this pull request works and fixes the issue(s)

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