feat: add widget screen search with proper back handling

[svenburkard]

Type of change(s)

• Bug fix
• Feature / enhancement
• Infrastructure / tooling (CI, build, deps, tests)
• Documentation

What changed and why

• Added a search bar to the widget screen so widgets can be filtered by app name and widget name.
• "Back" on widget screen closes search first and another "back" closes the widget screen.
• Widget search is also cleared after adding a widget.

Tests performed

• Searched widgets and verified live filtering.
• Long-press on a widget let you add it to home screen.
• Verified "back" behavior (first back closes search, second closes widget screen).
• Added a widget to home screen and reopened widget screen to verify search is cleared.

Before & after preview

issue56-widget-search.mp4

Closes the following issue(s)

• Closes Add search bar to widgets screen #56

Checklist

• I read the contribution guidelines.
• I manually tested my changes on device/emulator (if applicable).
• I updated the "Unreleased" section in CHANGELOG.md (if applicable).
• I have self-reviewed my pull request (no typos, formatting errors, etc.).
• I understand every change in this pull request.