The sceenshot didn't came through, but I checked the page source on the URL you provided. From what I can see, it is very likely that the wordpress header and the footer is completely missing in the theme files, (and) or there is a caching active as well.
Missing wp_head() and wp_footer() calls cause all the plugin scripts and files to be missing, resulting in a broken, unstyled search bar.
1. After placing the search bar somewhere, make sure to clear all layers of cache, including page, asset, minify, cloudlare, cdn etc..
2. Also, make sure to check if the:
– wp_head() function call is not missing from the theme header file (usually header.php in the theme directory)
– and the wp_footer() function call is not missing from the theme footer file (usually footer.php in the theme directory)
Those functions are very important for wordpress to run correctly, as they are responsible to print the enqueued CSS, JS and all other asset files and scripts as well, they must be included. I don't see any of the blueprints of the function outputs in the theme source, so there is a good chance that these are missing in the theme files.
Let me know what you can find!Best,
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