Feature 2: Implement "Content" Tab with Filtering

[fmontes]

Problem

The current Palette does not clearly separate different types of elements. Authors struggle to locate valid content quickly, especially with large lists. There is also no way to filter content inline.

Goal

Deliver a new "Content" tab that displays only valid content types for the current page and provides search/filter functionality so authors can find what they need faster.

Personas

• Content Author

Demo Expectations

In the bi-weekly demo, show the "Content" tab inside the new Palette UI. Prove that content types load from the backend endpoint and that filter/search works as expected, returning relevant matches.

[github-actions]

This issue is stale because it has been open 90 days with no activity. Remove stale label or comment or this will be closed in 30 days.

[rjvelazco]

We’re closing this ticket since the work was completed during the hackathon, and the related PR has already been merged: #33660