Hi,
The free plugin version is based on the native WordPress WP Query mechanism. It works fast for most people. If you have a lot of products and a lot of plugins, the native WordPress database structure can cause problems. it can’t be optimized well.
The solution is a custom, separated search index based on an inverted index. The Pro plugin version is based on such an index. Go to the plugin settings page (WooCommerce -> AJAX search form) and take a look at the features.
Best
Damian Góra