Automode examples including static node pools with neuron

**Is your feature request related to a problem? Please describe.**
Would like to see a pattern that shows how to use auto mode with various dynamic and static pool configurations for example with GPU/Neuron node groups.

**Describe the solution you'd like**
A pattern that deploys e2e and provides an example configuration for automode and node pools (or karpenter).

**Describe alternatives you've considered**
There are some examples in the blueprints repo for this, they should be promoted: https://github.com/awslabs/cdk-eks-blueprints/pull/1226

**Additional context**
Add any other context or screenshots about the feature request here.

Start by reviewing the promoted examples in awslabs/cdk-eks-blueprints PR 1226 and the repository's existing pattern structure. Add an end-to-end pattern showing Automode with dynamic and static node pools, including GPU or Neuron configurations, using node pools or Karpenter; done means the example deploys successfully and demonstrates these configurations.

Written by the indexing model from the issue text.