Federating into Azure, GCP and AWS with OIDC

Lately, I've been interested in how third party vendors can best authenticate into their customers' cloud accounts. The status quo in AWS is usually role assumption from the vendor's account to the customers', but what about GCP and Azure? Can OIDC be used to authenticate into all three clouds in approximately the same way? I think the answer is yes, and this blog post aims to show how to do so.