Identifying files associated with a contract

You could also leverage managed metadata data/the term store of this.  A little easier/more flexible that labels to update and would work for content stored across the organization as long as the column linking to the managed metadata was added everywhere.

The content type hub could help for this as you could publish down a "contract" content type that had that metadata column associated with it.

As far default taking with a specific ID based on a group.  Nothing comes to mind off the top of my head.  You could maybe cobble something together with Flow to run everytime a file is added/edited and check if it has an id and if not assign one.  The downside is that if documents could be added everywhere, the Flow would have to look at every possible location a document could be stored.