docs(search): Update search v-model

What does this MR do?

A small MVC for #869 (closed) where we update the docs to correctly show a button that can be used to manipulate the search value and use a more informative sentence to help communicate its purpose to a user.

Does this MR meet the acceptance criteria?

Conformity

• Code review guidelines.
• GitLab UI's contributing guidlines.
• If it changes a Pajamas-compliant component's look & feel, the MR has been reviewed by a UX designer.
• If it changes GitLab UI's documentation guidelines, the MR has been reviewed by a Technical Writer.
• If the MR changes a component's API, integration MR(s) have been opened in the following projects to ensure that the @gitlab/ui package can be upgraded quickly after the changes are released:
  • GitLab: mr_url
  • Customers Portal: mr_url
  • Status Page: mr_url
• Added the ~"component:*" label(s) if applicable.

Closes #869 (closed)