Can SchemaPlus change sitelinks?

SchemaPlus can’t change sitelinks, because sitelinks are randomly picked by Google. But schema can add a “Search bar” if a grand company implements it. The links below the search bar in the screenshot are called 'sitelinks'. You have no control over sitelinks - Google picks them for you and shows a list under your homepage as they wish. Unfortunately, schema is not related at all and you have no power to change the way your sitelinks look.

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​However, one thing we can suggest is to change the title of the "/collections/all" page from "Products" to "Shop All".
Google reads the title from <title></title> property on the page. If you change that property's value, Google will update the sitelink name accordingly.

Here is a discussion on the matter: https://community.shopify.com/c/shopify-discussions/how-to-change-header-of-this-shop-all-page/td-p/913400

Not every website is eligible. Google typically reserves the sitelinks search box for websites that receive a lot of branded inquiries. Check Google Webmaster Tools to determine whether your website qualifies. Google frequently notifies eligible website owners.

Google will lead users to your website's internal search results if you meet the requirements and the appropriate code is discovered on your homepage. The benefit is clear: by sending users to your own search results page rather than another Google page with advertisements from third-party websites, you may increase the number of clicks and visits while maintaining more control over the user experience.