Blue Green with Static S3 Website

Lambda@Edge (on origin request event) is your answer to route requests to different website variations on an s3 bucket. however, it's up to you how do you want to do the routing logic itself. For ex:

• If you want to have stickiness, then you should use Lambda@Edge also on viewer response event to set a cookie. forward this cookie in Cloudfront and use your Lambda@Edge router function to select the correct version.
• In the Lambda@Edeg router, you can make a network call to an external georgraphy replicated endpoint to to decide about the load balancing percentage. Replicated endpoints possibilities: dynamoDB global tables or Route 53 TXT records.