LinkControl – how to toggle opensInNewTab

This is covered in the documentation section directly above the one you linked, for value:

A link value is composed of a union between the values of default
link properties and any custom link settings.

The resulting default properties of value include:

• url (string): Link URL.
• title (string, optional): Link title.
• opensInNewTab (boolean, optional): Whether link should open in a new browser tab. This value is only assigned when not providing a
  custom settings prop.

So you’d need to include it in the value:

<LinkControl
    searchInputPlaceholder="Add Link"
    value={{
        url: attributes.link,
        opensInNewTab: attributes.opensInNewTab,
    }}
    onChange={(value) => {
        setAttributes({ link: value.url, opensInNewTab: value.opensInNewTab })
    }}
    settings={[
        {
            id: 'opensInNewTab',
            title: 'Opens in new tab',
        },
    ]}
    suggestionsQuery={{ type: "post", subtype: 'page' }}
/>