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I thought it came from the stack name.  I deleted the stack and recreated a 'develop' but /stage is still being appended to the api gateway endpoint url

That is the default `stageName` for API Gateway. You can configure the name, but there is no way to get a raw url without path with vanilla API Gateway - you need to provide your own DNS name, certs, and path mapping to accomplish that.

By the way, if you're up for the task, <https://github.com/pulumi/pulumi-awsx/issues/265> contains a code sample for how to accomplish this.