What does the project: key in module.info.yml do?
The Drupal 8 documentation for the keys to use in a .info.yml file doesn't mention it, but that is the same key documented in Writing module .info files (Drupal 7.x).


  project (Discouraged, packaging use only)
  
  Module maintainers should not use this at all. The packaging script on drupal.org will automatically place a string here to identify what project the module came from. This is primarily for the Update status module, so that Drupal installations can monitor versions of installed packages and notify administrators when new versions are available.


Drupal uses its value for building URLs when finding information about the module, or any file related to it. Technically, every Drupal core module could use the value of the project key to build a URL for something related to a module. I take the documentation gives the primary use of that key, since the Update module is present in all the last versions of Drupal.

I guess that, since its usage is discouraged, they don't document it for Drupal 8 to avoid users add it in their .info.yml files. It could help users creating a module that handles new keys in .info.yml files, though.
As for documenting it, I would document it just to avoid a developer creates a module that handles custom keys that conflict with the ones already used from Drupal core. I can understand this is seen as a use case that remotely interest developers, though.