From what I can see, this is going to be a cache related issue. If I check any other page on your site, the ajax search pro searchbar is displayed, while on the home page I see the default theme search. Clearing all layers of cache (page, CDN, Cloudflare, asset, varnish, browser cache etc..) will solve this issue for sure.
– Cached home page: https://i.imgur.com/GYdCTa6.png
– vs. any other page: https://i.imgur.com/dU70m6q.png
Another thing I noticed, that you have the results layout set to 'block', which is very likely not what you want, and will result in either pushing your header or weird result sizes. You can change that on the Layout Options -> Results layout panel: https://i.imgur.com/CXr2BTh.pngBest,
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