How do I build a k-prototype model on AWS and read the model output to Power BI?

You can build your k-prototype model in Amazon SageMaker. If you want an experience similar to Colab, you can use SageMaker Studio Lab. It is free and allows you to start sessions with limited CPU and GPU capacity. If you want more compute capacity, more storage capacity, or if you want to deploy your model, you can use the standard SageMaker service within your AWS account. You can then install the k-prototypes library you want to use and start building your model. For examples of how to build models in SageMaker, take a look at amazon-sagemaker-examples in GitHub.

This whitepaper explains how Power BI can integrate with various AWS services. SageMaker is not included, but S3, RDS, Redshift, and other services are covered. You can use SageMaker to run inference on your model and store the results in one of these services, then have Power BI read from these services. I'm not a Power BI expert, but if you can have Power BI connect to external APIs, then you could also deploy your model into a SageMaker endpoint. Together with Lambda and API Gateway, you can create an API which external tools can access to make inference requests to the model.