The share links feature is only available for Premium plans. The public_share_link field will be empty otherwise. Links will also stop working upon subscription downgrade.
A retro-active feature
If you upgrade to a Premium plan, your past Documents will include a share link.
When a Document is successfully generated, it will expose a public_share_link property that will contain a URL pointing to the PDF file. This link will not change over time and can safely be shared in an email or on a webpage.