The speed will be related to the complexity of the search (number of posts, number of form fields, number of terms in each field, whether you are using Auto Count or not) and the server.
Traditional hosting servers are frequently not configured to handle the data requests between the CPU, various caches and the disk drive. This is not a criticism of such hosting, they meet a need for most users. But, when you have large datasets, you may need to consider (potentially) more expensive hosting if you wish/need to avoid the speed/response issues. I am loath to make recommendations, but can, privately, if you wish. There is only one specialist who operate at the very top end of performance though, and, not unexpectedly, they are also not inexpensive. That would be Kinsta.
Because search results are dynamic, using a CDN for the results pages will also slow the process down, as they will not have a cache of the particular results requested.
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