## Summary
- Removed the unused `NewBadge` component from `ChatModeSelector.tsx`
- Removed "New" badge displays from Agent v2 and Plan mode options, as
these features are no longer new

## Test plan
- Verify the chat mode selector dropdown still renders correctly without
the "New" badges
- Confirm Agent v2 and Plan mode options are still selectable and
functional

🤖 Generated with [Claude Code](https://claude.com/claude-code)
<!-- devin-review-badge-begin -->

---

<a href="https://app.devin.ai/review/dyad-sh/dyad/pull/3113"
target="_blank">
  <picture>
<source media="(prefers-color-scheme: dark)"
srcset="https://static.devin.ai/assets/gh-open-in-devin-review-dark.svg?v=1">
<img
src="https://static.devin.ai/assets/gh-open-in-devin-review-light.svg?v=1"
alt="Open with Devin">
  </picture>
</a>
<!-- devin-review-badge-end -->
Co-authored-by: Will Chen <7344640+wwwillchen@users.noreply.github.com>
Co-authored-by: Claude <noreply@anthropic.com>