How to inform Chrome devtools that the tab was updated?

Whenever a Chrome tab is updated, I would like to inform devtools about the update. My background.js script looks like this:

var devtools_port = null;

chrome.runtime.onConnect.addListener(function(port) {
    var extensionListener = function (message, sender, sendReponse) {
        if (message.name == "init") {
            devtools_port = port;
            console.log(devtools_port);
        }
    }
    port.onMessage.addListener(extensionListener);
});

chrome.tabs.onUpdated.addListener(function(tab) {
    // This message is not delivered to devtools, WHY?
    devtools_port.postMessage({name:'Sending message to devtools'});
});

and my devtools.js looks like this:

var devtools_connection = chrome.runtime.connect({name: "devtools-page"});

devtools_connection.onMessage.addListener(function (message, sender, sendResponse) {
    // Console should print this, whenever a tab is updated, WHY DOESN'T IT?
    console.log("Devtools got message from background");
});

devtools_connection.postMessage({name: 'init'});

But for some reason, whenever I update the tab, the devtools_port.postMessage call in the background.js file seems to have no effect. Why is this the case?

For completeness, I have a devtools.html file with a <script src="devtools.js"></script> tag inside and my manifest file looks like this:

"manifest_version": 2,
"name": "Extension",
"version": "1.0",
"background": {
    "scripts": ["background.js"],
    "persistent": true
},
"devtools_page": "devtools.html"