@jmat75 as I suspected, the problem is from unloading the wrong JS file(s). If I load the URL like https://anothertree.com/?wpacu_no_js_unload (which for debugging purposes, loads back all the JS files), you will notice that it works fine.
Also, if you scroll to the bottom of the page, you will notice “X Fermer” showing up. This again is related to the wrong unloaded CSS file(s). If you load the URL like https://anothertree.com/?wpacu_no_css_unload (which for debugging purposes, loads back all the CSS files), you’ll notice that text disappearing. There are cases when you unload all the CSS/JS from a plugin (it could be the same here based on my experience), but it still loads HTML code that by default is hidden. When you unload its CSS, there’s no hidden rule applied anymore and it prints the hidden content when it shouldn’t. That content is printed whenever the modal/popup is triggered by the plugin. To unload a whole plugin (including any printed HTML, database queries, etc.), the Pro version is needed.
What you need to do for the page to load fine, is to remove the unloading rules one by one and see which is JS one that caused the search issue and the CSS one that caused the printing of that text at the bottom of the page. You can use the “Note:” option to leave some comments about the unloaded files in case you forgotten why you decided to unload certain files on various pages.