As I understand, you'd like to know how to fetch the domain name of your API Gateway API created by your CloudFormation stack and reference it as an output. Also, I can see that you're using AWS SAM to build your application.

In the processed template of your CloudFormation stack 'arn:aws:cloudformation:ap-southeast-1:407461997746:stack/days/f37dc1c0-27e2-11ec-ab94-0a12a8352912' there's an AWS::ApiGatewayV2::DomainName resource [1] with logical ID 'ApiGatewayDomainNameV23694ba20e6' which was generated by your 'Gateway' AWS::Serverless::HttpApi resource in the original template. You can reference this resource in your template's outputs by using its logical ID as a static value in a Ref function [2].

For example:
Outputs:
MyDomain:
Value: !Ref ApiGatewayDomainNameV23694ba20e6

Please note that unfortunately, the logical ID of the AWS::ApiGatewayV2::DomainName is not as predictable as other resources generated by AWS::Serverless::HttpApi such as:

• 'Gateway' for the AWS::ApiGatewayV2::Api resource.
• 'GatewayApiMapping' for the AWS::ApiGatewayV2::ApiMapping resource.
• 'GatewayApiGatewayDefaultStage' for the AWS::ApiGatewayV2::Stage resource.

Since the logical ID of AWS::ApiGatewayV2::DomainName is randomly generated when using AWS::Serverless::HttpApi, this logical ID only becomes available after processing the original template for the first time (which has already occurred in the provided stack). Also, If you update the domain name for this API, it will trigger a replacement update [3] and may cause the logical ID of this resource to change and require you to update the logical ID in any Ref functions in your template. My apologies if this behavior causes any frustrations on your end.

I hope I've been able to help, and as always, please don't hesitate to reach out if you have any further questions or concerns.

Links:
[1] https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/aws-resource-apigatewayv2-domainname.html
[2] https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/aws-resource-apigatewayv2-domainname.html#aws-resource-apigatewayv2-domainname-return-values
[3] https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/aws-resource-apigatewayv2-domainname.html#aws-resource-apigatewayv2-domainname-properties