Ok I've checked back the page and it is being loaded much master than before.
Did you do something on your end ? I cannot make comments on the database since I would need to install the query monitor plugin to check and see what exactly are the load times from the database.
This would essentially give me a better understanding of the database section of the load speed. However as mention the page is loading instantly for me and when I perform the search the results load instantly.
However your setup is fine but just a little information on the database is needed. If you're able to get the query monitor plugin installed . https://wordpress.org/plugins/query-monitor/
Great however i'm not seeing it active on this site, i'm not able to activate it myself since I don't have access to the plugins section.
However as mentioned the page with the search is loading Much Much faster for me.
Additionally if you're able to send a short video of what you are experiencing on your end that will help because from my end it appears everything is running fine.
Are you able get any load information on the Database from your host ?
The problems that you have alot of data being retrieved on this page because your filters are checking every post to ensure that it only displays the items that will produce a result in the filters.
I was wondering why the posts are being loaded up when its just the filters alone are on this page. However as mentioned when logged out the page loads up fine.