Hi,
I recommend checking this documentation article. The overall search speed depends on your local server performance, but there are ways described in that documentation to greatly optimize it.
I have run a few test queries on your back-end, to see how the server responds, and it seems to be a bit overloaded.
Even if I run completely empty test ajax queriest to the back-end (test means, not doing anything, just requesting the handler), it takes over 3 seconds: https://i.imgur.com/YEDxg22.png
So for the server to respond, it takes around 3.5 seconds, even if it does not do any work. That is a major problem, it should take around 0.5 – 1 seconds at best. I suggest investigating, if any plugins are doing some background requests during regular ajax calls, which delay the response time.