Hi,
The most likely cause might be, that the search shortcode might have been integrated into the theme header directly via editing the theme files. If the theme was updated, the change might have been reverted/updated.
The plugin update should not affect this in any way, as the shortcode/widget is rendered the same way across the versions.
I would rather not include an older version of the plugin, as downgrading will definitely cause issues and possible data loss. Reverting to older releases is only recommended if you have a database and file archive.
First, I suggest checking if the automatic theme search replacement feature is enabled – maybe the devs used that feature for the override.