Search function not working mobile

Hi,
We are currently trying to use Ivory Search on this page on mobile: https://entwicklungsseite-stiftung.de/

In the Menu Search Settings we have activated right mobile menu and under Settings > display search form in site header + the page uses cache.
Unfortunately, the search is not displayed and may have a conflict with the mobile menu plugin from Freshlight Lab.

Is there a way to use and display the search in the plugin? Or is there an optional way to work with the shortcode in the menu and place it there?

Many thanks and best regards
Benni

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