Google continues to add features to the new Sites app. One that was available in Classic Sites is the ability to embed another website in a Google Site. Based on feedback, Google has now added the ability to embed an entire webpage as an iframe in a new Google Site. This allows you to pull in content from other websites and Google tools like Apps Script and Data Studio. Select Embed URL from the Insert menu.
Note: This only works if that webpage allows it to be embedded. Otherwise, only a link to the webpage is inserted.