How can I disable ajax seach bar in the header?

Hi guys, sorry for this but it's driving me crazy.

I am switching from e-commerce to blog-only type site. I am disabling woocommerce for now but the search bar in the header stays there as a shortcode. I checked my php files, widgets and menus but couldn't find where it is getting that from.

Could you please help me to completely disable it?

thank you.