On line 30 of _panels.scss you have a CSS rule for .search-form { padding: 0 12px; } that is interfering with the WordPress media library search input.

Heres a couple screenshots detailing the bug using the Tailor advanced plugin:

As you can see in the 3rd screenshot I have commented out the style rule inside the chrome developer tools and the search bar is visible again. I will say that if you tab inside the media library modal till you hit the search bar it focuses itself, but it seems like this is the root of the problem.