> Deeply embedded meaning they have a deep network of sources, or deeply embedded meaning they are working in concert with American intelligence services?

¿Por qué no los dos? Access Journalism easily explains both. Journalists know where their bread is buttered - members of the "deep network of sources" may occasionally call in favors, or drop breadcrumbs leading journalists to a specific, preselected destinations.

A recent HN thread led me down the rabbit-hole that included an opionion of some (British) monarchy insider. They observed that the monarchy would sometimes leak a story to the press with specific framing, and then the article would include the usual "We have reached out to the royal family for comment" spiel, and yet the entire article is the comment by the royal family. On the other side of the Atlantic, it wasn't too long ago that JD Vance was outed as the unnamed source of a story that the Trump admin subsequently attempted to sue for on national security grounds.