Hi,
Thank you for the proper details and explanations, it helps me a lot.
I’ve looked at your configuration, it looks perfectly correct to me. I have measured the response times, it was around 1.5 – 2.5 seconds. I would say it is reasonable, given that the page load time is over 8 seconds in total. I’ve also checked the performance tracker, to see if the search query runs okay, and it is finished within 0.08 seconds in average, which is extremely fast: https://i.imgur.com/f8RkIdk.png
This means, that the overall search process only takes about 0.08 seconds every time from the whole 1.5-2.5 response time. The rest of the time is taken by WordPress loading up itself, loading the plugins/themes etc..
In addition, I have enabled the search cache, and the image cache, which will build up during search requests, making it a bit faster, as it terminates the whole ajax process much earlier, preventing further loading of modules, gaining additional speed: https://i.imgur.com/4wUKYs4.png
If you feel that the search results get less relevant, then turn off this option.
Right now the cached queries run below 1.5 seconds, I don’t thing there is any more optimization possible from the plugins perspective, the rest is up to WordPress and the server performance.