refactor: make change in app sources reflect on search results

Description

When app sources (Common apps, open-source, or PWA) are checked/unchecked in App Lounge Settings, the search results reflect those change — shows/hides results from those sources.

Screenshots

Screen_recording_20250918_183338-App_Lounge

Technical details

Tests

Issues

https://gitlab.e.foundation/e/os/backlog/-/work_items/3665

10 commandments of code review

👪 ❤️ https://gitlab.e.foundation/groups/e/-/wikis/contribute/development-processes/code-review-guidelines