Starring is currently done with this tag

<star:star type="atlassian-quicksearch" stringKey1="${this.repository}" stringKey2="${this.query}" />

Unfortunately, for cross-repository searches this.repository is empty and the class converts an empty string passed through to null

When a repository is selected and the user is logged in, they are shown the star and can set a favourite.

Maybe all that needs doing is adding a check to see if this.repository is empty and setting it to "All repositories" once more?