I don't see you made any of the suggested changes in the documentation, the configuration is still the default.
Moreover I have measured the search speed and it's around 3 seconds every time: https://www.youtube.com/watch?v=cl4nfmtS9pc&feature=youtu.be
It is still performs faster than your overall random non-cached (first time view) site load time, which is 6 seconds:
The initial server response was 5.05 seconds (6.05 overall with rendering), so it took around 5 seconds for wordpress to generate the page. The search however responds in around 3, so it is still almost 40% faster than your server response.
With the optimisations it could get much better.Best,
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