Hi!
There is a guide in the knowledge base for safe upgrading, as well as in the documentation:
https://wp-dreams.com/knowledge-base/updating-from-older-versions/
http://wp-dreams.com/demo/wp-ajax-search-pro3/docs/#important_upgrade_notes
I believe you missed one step. The cache options have changed in the new version, so there is a possibility of database inconsistency. Since you give me access I did solve this for you, by simply saving the cache options without change. It should be working now correctly.