One of the big advantages of JSON-LD for SEO is that is can provide structured information to Google indicating how customers can perform a search on your site. This means Google may choose to display your brand’s search results with a Sitelinks Searchbox like this:
JSON-LD for SEO will setup the structured data for your Shopify store’s search so that Google can find it. However it’s important to note that JSON-LD for SEO cannot guarantee that Google will display this search box when someone searches for your brand.
Ultimately the decision to display this search box is made by Google’s algorithms, which they don’t share publicly.