fix(app): updates to project selector

[arvsrn]

Issue for this PR

Closes #140

Type of change

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

What does this PR do?

• Fix bug where project search input gets deselected after every keystroke
• Update check icon, alignment
• Update border radii on the trigger and menu items
• Adds keyboard navigation to the project picker (arrows to cycle, enter to select; selected item has bg-overlay-hover; first item is selected by default)
• Added pressed state to dropdown trigger

How did you verify your code works?

• Ran the app locally and verified the updated UI manually
• Ran type checks locally (bun turbo typecheck)

Screenshots / recordings

Checklist

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

If you do not follow this template your PR will be automatically rejected.

[github-actions]

Hey! Your PR title updates to project selector 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.