Checks if the current request is a WP REST API request.

is_rest.php

<?php

if ( !function_exists( 'is_rest' ) ) {
	/**
	 * Checks if the current request is a WP REST API request.
	 *
	 * Case #1: After WP_REST_Request initialisation
	 * Case #2: Support "plain" permalink settings
	 * Case #3: It can happen that WP_Rewrite is not yet initialized,
	 *          so do this (wp-settings.php)
	 * Case #4: URL Path begins with wp-json/ (your REST prefix)
	 *          Also supports WP installations in subfolders
	 *
	 * @returns boolean
	 * @author matzeeable
	 */
	function is_rest() {
		$prefix = rest_get_url_prefix( );
		if (defined('REST_REQUEST') && REST_REQUEST // (#1)
				|| isset($_GET['rest_route']) // (#2)
						&& strpos( trim( $_GET['rest_route'], '\\/' ), $prefix , 0 ) === 0)
				return true;

		// (#3)
		global $wp_rewrite;
		if ($wp_rewrite === null) $wp_rewrite = new WP_Rewrite();
			
		// (#4)
		$rest_url = wp_parse_url( trailingslashit( rest_url( ) ) );
		$current_url = wp_parse_url( add_query_arg( array( ) ) );
		return strpos( $current_url['path'], $rest_url['path'], 0 ) === 0;
	}
}