Migrate SearchRouter.tsx from useOptionsList to useFilteredOptions

[mountiny]

Problem

SearchRouter.tsx currently uses the useOptionsList hook from OptionListContextProvider, which causes unnecessary background recalculations on every personal details or reports change.

This is part of a larger effort to remove OptionListContextProvider entirely. See parent issue #82193 for full context.

Solution

Replace useOptionsList with useFilteredOptions following the pattern established in PR #74071 (NewChatPage migration).

Current usage:

• Properties used: areOptionsInitialized only
• Called with: no arguments
• File: src/components/Search/SearchRouter/SearchRouter.tsx

How areOptionsInitialized is used:

• Combined with isRecentSearchesDataLoaded into shouldShowList flag
• Controls conditional rendering: shows SearchAutocompleteList when true, shows OptionsListSkeletonView when false

Migration steps:

1. Replace import {useOptionsList} from '@components/OptionListContextProvider' with import useFilteredOptions from '@hooks/useFilteredOptions'
2. Replace useOptionsList() call with useFilteredOptions({ enabled: true })
3. Replace areOptionsInitialized with !isLoading in the shouldShowList computation
4. The rest of the conditional rendering logic should work as-is

Note: This component only uses areOptionsInitialized for gating visibility. The actual options data is consumed by SearchAutocompleteList (a separate migration issue). These two migrations are independent.

Complexity: Simple

Reference PR: #74071

Tests

• Verify the search router opens and shows the autocomplete list correctly
• Verify the skeleton loading view shows while options are being computed
• Verify search functionality works end-to-end
• Verify no errors appear in the JS console
• Test on all platforms (iOS, Android, Web, Desktop)

[hoangzinh]

we can close this issue. PR is deployed to Prod