The object app
is a UiApp instance, not an html content. One should consider it more as a command that tells the Google server to generate an html page using GWT toolkit so obviously (as you said) the code you tried can't work.
If you try to get the content of the shown page using something like
var htmlContent = UrlFetchApp.fetch('https://script.google.com/macros/s/AKf------Z1BBusUdHBmbWI-eqNjM/exec').getContentText();
you will see that it looks like anything but an understandable html code , plus you will meet issues with authorizations, warning messages and/or 'loading' messages...
As far as I know there is not way to capture the html content from a webapp in a form that would be compatible with the site method page.setHtml
, at least not using Google Apps Script methods.
maybe some hack somewhere but not that I know...