retrieve all active tabs content

To get the DOM for a specific tab, you would need to use content scripts communications.
https://developer.chrome.com/extensions/messaging

If you need to send a request from the extension to your content script,

chrome.tabs.getSelected(null, function(tab) {
  // Send a request to the content script.
  chrome.tabs.sendRequest(tab.id, {action: "getDOM"}, function(response) {
    console.log(response.dom);
  });
});

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In the content script, if you need to listen for those events coming from the extension, use this code:

chrome.extension.onRequest.addListener(function(request, sender, sendResponse) {
 if (request.action == "getDOM")
   sendResponse({dom: "The dom that you want to get"});
 else
   sendResponse({}); 
});

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And look this article:
https://developer.chrome.com/extensions/extension#event-onRequest
And this article:
https://developer.chrome.com/extensions