There are number of things you can do, but ultimately the search performance will reflect the server performance. WordPress also does load all the plugins before executing ajax requests – and if this environment load caused by other plugins as well is high, then it will affect the ajax response time greatly.
You can find a whole chapter in the documentation about performance tweaks. Also, check out the built-in performance tracker, it will give you an insight how much time the search process needs. If the number on the tracker is significantly lower than the actual response on the front-end, it means that the delay is not caused by the search plugin, but the loading of other plugins/themes within the ajax request.
If however the performance tracker reveals that the search performance is indeed problematic, not caused by other plugins, let me know, and I will do a quick debugging on the code to check what’s holding back the engine.Best,
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