In the past few years, we have covered plenty of amazing Elementor plugins and themes here. Searcher is also worth a look. It is an Ajax search plugin with asynchronous and regular requests. In asynchronous mode, results are displayed as you are typing. Searcher is ready for WooCommerce. It should work well with any theme made for Elementor.
Searcher is ready for various languages, including RTL languages. It has a responsive design and lets you change icons easily. This plugin lets you change alignment, empty search placeholder, post style, request delay and other settings.