EmbedPress has an auto-embed feature that tries to embed all URLs found in posts. This can cause problems with Relevanssi: searches can take a very long time when EmbedPress tries to fetch all outside URLs.
The solution is simple: you can disable this feature during Relevanssi excerpt creation. Add this snippet to your site:
add_action( 'relevanssi_pre_the_content', function() {
remove_filter('the_content', ['\\EmbedPress\\Ends\\Front\\Handler', 'autoEmbedUrls']);
} );