Share data between two GAS scripts embedded at a Google site

Question

I'm pretty new in this whole Google Apps/Sites/Add-ons so I'm not sure if what I want is possible.

I have a Google Apps Script that is published as "anyone, even anonymous" and runs under my account. The script saves something to a user cache like this

function firstScriptCalledFromButton() {    
  var cache = CacheService.getUserCache();
  cache.put('info', 'my info');
  return true;
}

this script is then embedded in a (new) Google site.

Then I have my second script that tries to read the user cache, again published as "anyone, even anonymous" and again embedded at the same Google site as the first one, different frame though (I'm not sure how it's handled there if this is a real iframe or not).

function secondScriptCalledFromButton() {
  var cache = CacheService.getUserCache();
  var data = cache.get('info'); // this is always null     
  console.log('Here I expect to see cached data ' + data);
  return data;
}

Is this even possible? Any other option? I tried [documentCache][1] with the same result.