the following will help identify how rendering the HTML view is done in SFMC Email Studio / content builder by actually rendering an email like it is shown in the system - only without the additional "edit me" overlays that pop up there
const uri = '/asset/v1/content/assets/4936/views/html';
const response = await this.client.rest.get(uri);
4936 in this example is the asset id (not the legacy id)