This is a very neat trick because you can definitely ask an API for JSON via accept header (https://developer.mozilla.org/en-US/docs/Web/HTTP/Headers/Ac...) while being compliant with simple requests by using query strings and/or multipart/form for routes option.
At this point when I see the Algolia search box on a site, I know I won't get a full search experience it will be slightly crippled with a custom interface and a forced auto-complete with JS only interface support.
An example of this is vuejs.org vs developer.mozilla.org. With Mozilla dev site, I have 'mdn' as my search key (both Firefox and Chrome) and I can type "mdn grid-template-columns" and I get results. With vuejs.org and Algolia, I have to go through multiple clicks and visual hunt and peck to find what I am looking for. It's a productivity killer.
This is a good example why computer experience of today is so terrible:
"Never run a changing system" is dead. Systems are changing all the time.
I'm wondering whether the http://hn.algolia.com/opensearch.xml configuration could help here, might need to tweak it a bit.
(Algolia charges thousands of dollars for some of their services and I find it the worst search system currently used on popular sites.)