add-search-to-menu (Ivory Search)

https://wordpress.org/plugins/add-search-to-menu/

Ivory Search is a simple to use advanced WordPress search plugin.

It enhances the default WordPress search and also allows you to create new custom search forms.

With Ivory Search, you can create an unlimited number of search forms and configure each search form individually to customize WordPress search and perform different types of searches on site content.

How to set up article - 
https://www.wpbeginner.com/plugins/how-to-add-a-search-bar-to-wordpress-menu-step-by-step/

Note:
Search in menu did not work with Oxygen
"Navigation menu location is not registered on the site."