* Redesign mobile search field as a shared, raised component
- Extract MobileSearchField from duplicated Search icon + TextInput + clear
button markup in worktree list and tasks screens into a reusable component
- Give the field a raised bgRaised shell with focus/disabled states so it
reads as a tappable control instead of blending into panel chrome
- Fix delayed autoFocus via InteractionManager + timeout so the keyboard
reliably appears after the search bar opens
- Preserve per-screen clear behavior (preset/query fallback for GitHub,
project-view filter) via configurable showClear/onClear props
* Simplify GitHub project search state checks and fix stuck clear button
- Extract `isGithubProjectSearch` to dedupe repeated `provider === 'github' && githubMode === 'project'` checks
- Fix showClear so an explicit empty applied override doesn't leave the clear button visible forever