I am aware AWS has sign-in UI for ios and android apps, But is there a similar functionality for web apps as well?
If you mean sample Apps, indeed for ios and android, we have provided sample apps for user pools (if that is the service you are looking for). For Javascript, there are a couple that either external developers or solutions architects have written. Links below:
https://github.com/awslabs/aws-cognito-angular2-quickstart
https://github.com/aws/amazon-cognito-identity-js/issues/123