Thank you for the details!
The issue was, that your database contains a huge amount of content, and the database server was not able to look for matches faster.
Since you give access, I have made a few adjustments, to improve the performance greatly:
– I enabled and generated the index table engine. It greatly helps to increase the performance and speed. It indexed over 500 000 keywords: https://i.imgur.com/5Ld5IVL.png
– Also enabled the custom ajax handler: https://i.imgur.com/IG2m6Zu.png
These resulted in a 25x increase of performance. You can read more about performance improvements on this documentation article: Improving search performance
The search should have now a much better performance.
1. Exact matching
I would not recommend using that option in your case – as it automatically uses the Regular engine (instead of the Index table), which will greatly decrease the performance.
In your configuration the main and secondary keyword logics are set exact word matching, which is much more precise with the current configuration as the exact matching: https://i.imgur.com/14mi7vk.png
Exact matching checks if the content, title etc.. contains the keywords exactly as entered – regardless if it's within the content or anywhere else, therefore it's slower, and cannot use the index table, as it has to search the posts table – which is not optimized for searching.
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