Looks like you need put search box after navigation block and use css to make display it in one line, beckouse html/topmenu.phtml block don't print their child's
<move element="top.search" destination="page.top" after="catalog.topnav" />
or overwrite html/topmenu.phtml to
<?php $columnsLimit = $block->getColumnsLimit() ?: 0; ?>
<?php $_menu = $block->getHtml('level-top', 'submenu', $columnsLimit) ?>
<nav class="navigation" role="navigation">
<ul data-mage-init='{"menu":{"responsive":true, "expanded":true, "position":{"my":"left top","at":"left bottom"}}}'>
<?php echo $_menu; ?>
</ul>
<?php echo $block->getChildHtml() ?>
</nav>
Also feel free to create issue on github or create pull request with fix.