Nit pick. Kubernetes doesnt run docker containers. It run containers that conform to the Open Container Initiative ( OCI ) . Docker is a licensed brand name.
Plenty of larger clusters exist, but this usually requires extensive tuning (such as entirely replacing the API registry). And obviously the specific workload plays a large role. Kubernetes is actually quite far from supporting larger clusters out of the box, though most releases include some work in that direction.
Ah yeah I could be wrong. In my early days at Airbnb, I recall someone doing an internal test to prove it could scale to 10k servers, but this was back in 2016 and I wasn't the one doing the test.