Hi,
If the class does not exist, that may indicate that you might be trying to access it before the plugin is loaded.
It was indeed moved to a different file in the most recent patch: wp-content/plugins/ajax-search-pro/src/server/Query/SearchQuery.php
However the ASP_Query class alias is autoloaded, that should still work.
If for some reason it does not, then please use the namespace variation new WPDRMS\ASP\Query\SearchQuery();
I will update the documentation in a minute with the correct path and namespace. Thanks for letting me know!