fix(app): show reasoning selector in v2 prompt

[Ogyeet10]

Issue for this PR

Closes #29051

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

The v2 prompt input used by non-prod desktop builds rendered the model picker but not the existing model variant selector. That made models like GPT-5.5 show as selected without a visible control for reasoning level.

This adds the same variant selector to the v2 prompt controls and reuses the existing variant list, selection, and cycle command behavior.

How did you verify your code works?

• bun typecheck from packages/app
• bun --cwd packages/desktop build
• bun turbo typecheck from the push hook

Screenshots / recordings

Not included. Verified locally in the desktop dev app.

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

[github-actions]

Thanks for your contribution!

This PR doesn't have a linked issue. All PRs must reference an existing issue.

Please:

1. Open an issue describing the bug/feature (if one doesn't exist)
2. Add Fixes #<number> or Closes #<number> to this PR description

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[github-actions]

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