Elementor Custom Query Filter using New Search Widget. Search widget supports ajax hitting the Rest Endpoint

functions.php

<?php
// Here we use tax query but meta_query is also possible
// Unfortunately, there is no way to merge Wordpress default search behaviour, meta_query and tax_query using OR
// that I could find.
// Default behaviour for merging these queries are AND.
// Custom Elementor Query for Search
function mpons_custom_property_search_query($query) {

	// Get the search term from the WP_Query object
    $search_term = $query->get('s');

	//  load the terms using LIKE
	$termIds = get_terms([
		'name__like' => $search_term,
		'fields' => 'ids'
	]);
	
	// Get current tax Query
	$tax_query = $query->get('tax_query');

	// If there is no tax query when this filter runs, it should be initialized as an empty array.
	if (!$tax_query) {
		$tax_query = [];
	}

	// Append our tax query
	$tax_query[] =[
		'taxonomy' => 'location',
		'field' => 'id',
		'terms' => $termIds,
	];
	
	// AND relation, there is no way I could find for the OR relation
	$query->set('s', $search_term); // not necessary since this is default Wordpress search behaviour, it is here for demonstration
	$query->set('tax_query', $tax_query);
}
// Hook the custom query into Elementor
add_action('elementor/query/custom-property-search-query', 'mpons_custom_property_search_query');