"content_scripts": [{
    "matches": ["http://myUrl1.com/*"],
    ...
}]

"content_scripts": [{
    "matches": [ "http://*/*", "https://*/*" ],
    ...
}]

"permissions": [
  ...
  "http://*/*"
  "https://*/*"
],
"background": {
    "scripts": ["background.js"]
},
...

const ALLOWED_URL = '...'; // Разрешенный URL

// отслеживаем изменение во вкладках
chrome.tabs.onUpdated.addListener(function(tabId, changeInfo) {
  if(changeInfo.status === 'completed' && changeInfo.url === ALLOWED_URL) {

    // запускаем content-script
    chrome.tabs.executeScript(tabId, {
      file: 'content-script.js'
    });
  }
});