fix(desktop): Remove Cursor Unfocused Prompt Input

[dbpolito]

What does this PR do?

Remove the cursor from the prompt input when focus moves to another element, addressing an issue with cursor visibility in certain environments.

How did you verify your code works?

Currently if you click some elements, or sometimes when you cmd + tab, the focus leaves the prompt input, but the cursor is still there, for example, focus the prompt input, and click on session breadcrumb that opens sessions:

This works on web version, but on tauri version of mac has weird behaviors.

So if you focus prompt, click there, and paste an image from the clipboard, this still happens:

Also tested moving cursor to a new input like terminal, works fine.

[github-actions]

Hey! Your PR title Desktop: Remove Cursor Unfocused Prompt Input doesn't follow conventional commit format.

Please update it to start with one of:

• feat: or feat(scope): new feature
• fix: or fix(scope): bug fix
• docs: or docs(scope): documentation changes
• chore: or chore(scope): maintenance tasks
• refactor: or refactor(scope): code refactoring
• test: or test(scope): adding or updating tests

Where scope is the package name (e.g., app, desktop, opencode).

See CONTRIBUTING.md for details.

[github-actions]

The following comment was made by an LLM, it may be inaccurate:

No duplicate PRs found

[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

See CONTRIBUTING.md for details.