feat(search-client): replace input output decorator technique with signals

[vaibhavbhalla2505]

Description

This pull request refactors the SearchComponent in the Angular search library to use Angular's new signal-based input and output APIs, and replaces direct property access with computed signals throughout the component and its template. This modernizes the component, improves reactivity, and simplifies input/output handling. Several internal methods and template bindings are updated to use the new reactive patterns, and legacy input/output decorators and setters are removed.

Key changes include:

Migration to Angular Signals:

• Replaced all @Input and @Output decorators in search.component.ts with the new input() and output() signal-based APIs, and removed legacy setters/getters. All references to configuration and templates in the component and template now use computed signals (e.g., cfg(), titleTemplate()). [1] [2] [3]

• Updated the component's logic to use effect() for reacting to changes in inputs, such as updating models, adapting the search provider, and handling custom search events.

Fixes #61

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Intermediate change (work in progress)

Checklist:

• Performed a self-review of my own code
• npm test passes on your machine
• New tests added or existing tests modified to cover all changes
• Code conforms with the style guide
• API Documentation in code was updated
• Any dependent changes have been merged and published in downstream modules