I'm an Ex-Google SRE. Kubernetes is not Borg, will never be Borg, and Borg does not need to borrow from k8s - Most of the "New Features" in K8s were things Google had been doing internally for 5+ years before k8s launched. Many of the current new features being added to k8s are things that Google has already studied and rejected - It breaks my heart to see k8s becoming actively worse on each release.
A ton of the experience of Borg is in k8s. Most of the concepts translate directly. The specifics about how borg works have changed over the years, and will continue to change, but have never really matched K8s - Google is in the business of deploying massive fleets, and k8s has never really supported cluster sizes above a few thousand. Google's service naming and service authentication is fully custom, and k8s is... fine, but makes a lot of concessions to more general ideas. Google was doing containerization before containerization was a thing - See https://lkml.org/lkml/2006/9/14/370 ( https://lwn.net/Articles/199643/ doesn't elide the e-mail address) for the introduction of the term to the kernel.
The point of k8s was to make "The Cloud" an attractive platform to deploy to, instead of EC2. Amazon EC2 had huge mindshare, and Google wanted some of those dollars. Google Cloud sponsored K8s because it was a way to a) Apply Google learnings to the wider developer community and b) Reduce AWS lock-in, by reducing the amount of applications that relied on EC2 APIs specifically - K8s genericized the "launch me a machine" process. The whole goal was making it easier for Google to sell it's cloud services, because the difference in deployment models (Mostly around lifetimes of processes, but also around how applications were coupled to infrastructure) were a huge impedance to migrating to the "cloud". Kubernetes was an attempt to make an attractive target - That would work on AWS, but commoditized it, so that you could easily migrate to, or simply target first, GCP.
Thank you for the exhaustive depiction of the situation. Also an ex SRE from long ago, although not for borg. One of the learnings I took with me is that there is no technical solution that is good for several orders of magnitude. The tool you need for 10 servers is not the one you need for 1000, etc.