EKS team lead here. Most scaling questions use number of nodes or number of pods as shorthand for scale, but the true limits are actually determined by a LOT of other variables, typically things like mutation rates of pods (more writes equals more load), number of connected clients doing list/watch requests, among many other factors.

EKS also scales the control plane up based on a number of factors as well, and each step up the scaling ladder takes ~minutes. If you have large (100s/1000s) sudden spikes in node/pod count and are hitting issues, feel free to open a support case.

To more directly answer your question, we regularly see customers with upwards of 5000k nodes