Hi it depends on few factors if you can answer

1.Whether the document had never been shared publicly, or if it was at some point before being restricted.

2.Whether LinkedIn showed only the title and a thumbnail, or any part of the document content.

3.Whether your friend is part of a Google Workspace domain (e.g., company/org), or a regular Gmail user.

apparently the document was briefly public.

When a Google Doc is briefly made public, services like LinkedIn can access its metadata — such as title and thumbnail — through standard Open Graph tags. LinkedIn caches this metadata for about a week. Even if the doc is later made private or restricted to a specific Google Workspace, LinkedIn will still show the cached preview. It doesn’t mean LinkedIn has special access or that Google is leaking anything; it’s just a consequence of how caching and metadata scraping work. This behavior is expected and not considered a security issue.

Wouldnt surprise me if they let Linkedin have some access to parts of the doc so they could show a preview. Does the same thing happen if you share it on Instagram or Facebook?

Lately I've seen people share full copyrighted books straight on LinkedIn, not sure if that's related.