A method for detecting when WP_Query is being run for a REST API call.

api-wp-query.php

<?php

/**
 * Filter allowed query vars for the REST API.
 *
 * This filter allows you to add or remove query vars from the final allowed
 * list for all requests, including unauthenticated ones. To alter the
 * vars for editors only, {@see rest_private_query_vars}.
 *
 * @param array {
 *    Array of allowed WP_Query query vars.
 *
 *    @param string $allowed_query_var The query var to allow.
 * }
 */
add_filter( 'rest_query_vars', 'filter_rest_query_vars' );
function filter_rest_query_vars( $valid_vars ) {

	// Add our REST API flag
	$valid_vars[] = 'wp_rest_api';

	return $valid_vars;
}

/**
 * Filter the query arguments for a request.
 *
 * Enables adding extra arguments or setting defaults for a post
 * collection request.
 *
 * @see https://developer.wordpress.org/reference/classes/wp_user_query/
 *
 * @param array           $args    Key value array of query var to query value.
 * @param WP_REST_Request $request The request used.
 */
add_filter( 'rest_post_query', 'filter_rest_post_query', 10, 2 );
function rest_post_query( $args, $request ) {

	// FYI: 'post' in the filter name, 'rest_post_query', is the
	// name of the post type and can be interchanged.

	// Add a flag for us to use later
	$args[ 'wp_rest_api' ] = true;

	// Return the filtered query args
	return $args;
}

////////////
// ABOVE IS ALL YOU NEED FOR DETECTION
////////////
// BELOW IS AN EXAMPLE OF HOW YOU WOULD IMPLEMENT THE DETECTION IN ANOTHER FILTER
////////////

/**
 * Filter all query clauses at once, for convenience.
 *
 * Covers the WHERE, GROUP BY, JOIN, ORDER BY, DISTINCT,
 * fields (SELECT), and LIMITS clauses.
 *
 * @since 3.1.0
 *
 * @param array    $clauses The list of clauses for the query.
 * @param WP_Query &$this   The WP_Query instance (passed by reference).
 */
add_filter( 'posts_clauses', 'filter_posts_clauses', 10, 2 );
function filter_posts_clauses( $pieces, $query ) {

	// Only filter the clauses if we're using the REST API
	if ( ! $query->get( 'wp_rest_api' ) ) {
		return $pieces;
	}
	
	// Filter the clauses
	
	// Return the pieces
	return $pieces;
}