This is not something that can be achieved in the native SSJS, AMPScript functions nor by the SOAP API. You will need to utilize the REST API to get this. This is because Content Builder assets are stored elsewhere than classic, which is where the native functions and SOAP are aimed at.
I would utilize the 'GET Asset' REST Call.
Sample of call (using SSJS - assuming you gathered the auth Token already):
var authToken = "Bearer: " + accessToken;
var url = 'http://{{yourendpoint}}/asset/v1/content/assets?$filter=Name%20like%20'{{yourEmailName}}'';
var headerNames = ["Authorization"];
var headerValues = [authToken];
var response = HTTP.Get(url, headerNames, headerValues);
In the JSON you receive via the response, you will find the email content in items > views > html > content
e.g.
{
"items": [
{
"views": {
"html": {
"content": "{{yourHTMLContent}}"
}
}
}
]
}