Your value prop is the wrong format. From <LinkControl>‘s README:

value

• Type: Object
• Required: No

Current link 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.

If the link’s actual title & “opensInNewTab” properties are relevant to your ends, then you should store the whole value in attributes in the handleLinkChange() function. Otherwise, specifying the linkText attribute should be sufficient. As mentioned in the README, you can also specify a settings prop to suppress the “Opens in New Tab” toggle (or add additional toggles):

            <LinkControl
                onChange={ handleLinkChange }
                value={ { url: linkURL, title: linkText } }   
                settings={ [] }    
            />