Inject content-script from browser-action and communicate with it

browser_action.js

// Get the current active tab
chrome.tabs.query({ active: true, currentWindow: true }, function (tabs) {
  // Send message to check whether the script has already been injected
  chrome.tabs.sendMessage(tabs[0].id, "ping", function (response) {
    // If no message handler exists (i.e. content-script hasn't been injected before),
    // this callback is called right away with no arguments, so ...
    if (typeof response === "undefined") {
      // ... inject content-script (null means current active tab)
      chrome.tabs.executeScript(null, { file: "content_script.js" });
    }

    //# Register events or other stuff that send messages to the content-script
  });
});

content_script.js

// Listen for messages from browser-action or background script
chrome.runtime.onMessage.addListener(function (request, sender, sendResponse) {
  var response;
  
  // Message to check whether this script has been injected
  if (request === "ping") {
    // "Yeah, we're good"
    response = "pong";
  }
  else {
    //# Do whatever needs to be done
    //# response = ...
  }
  
  sendResponse(response);
});