Does autocomplete hit origin on every request?

Basically, yes, for each time autocomplete suggestions are shown to the user they will have to be retrieved from the Drupal site. There are potentially a few methods for alleviating the load, though:

• For one, you can increase the delay after typing before autocompletion gets triggered to reduce the number of requests.
• Secondly, client-side caching is already built into Drupal’s autocomplete (unless I’m mistaken) – however, it’s only for that page, so this will not help much.
• If you are using a reverse proxy like Varnish it should also be possible to configure that to cache autocomplete responses. Note, though, that the cache hit rate for search requests is often rather poor, as there are of course a lot of different keywords people could enter (at least on most sites).
• Finally, there is the “Custom script” suggester which you can use to point the autocomplete functionality to a different (non-Drupal) endpoint, which can help to decrease response times (and server load per request) significantly. Since this is advanced functionality, which will also require some custom code, it is usually not available. See the README.md file and CustomScript.php for details.

With custom code, you could of course also try other ways of circumventing the REST request to the autocomplete endpoint, like sending some frequent user inputs and their suggestions as JSON right with the initial page request, or storing received autocomplete responses in local storage to get caching across pages.

I’m leaving this open for now in case others have more suggestions or personal experience, but feel free to mark as fixed if this already answers your question.