fix(ui): sync SearchBar value with defaultValue changes

[Mayankaggarwal8055]

Fixes #65053

Problem

SearchBar initializes its internal state from defaultValue but does not update when defaultValue changes (e.g., via URL query params or navigation).

This causes the input value to go out of sync with the actual filter state.

Solution

Synchronize internal state with defaultValue using useEffect, ensuring UI reflects current filter state while preserving user input behavior.

Tests

• Added test to verify syncing when defaultValue changes
• Added test to ensure user typing is not overridden unnecessarily
• Existing debounce and clear behavior preserved