Cannot get background.js to work with new manifest v3 notation

Question

I wrote some extensions a while ago with manifest v2 and now wanted to write a new one but somehow I cannot get the background.js to run. Meaning that the script does seemingly not execute at all.

manifest.json

{
    "manifest_version": 3,
    "name": "extension",
    "description": "example",
    "version": "1.0",
    "permissions": [
        "scripting",
        "tabs"
    ],
    "host_permissions": ["https://*.example.com/*"],
    "background": {
        "service_worker": "background.js"
    },
    "action": {
        "default_title": "Click Me",
        "default_popup": "popup.html"
    }
}

content_script.js

chrome.runtime.sendMessage({
  url: window.location.href,
})

background.js

chrome.runtime.onMessage.addListener(function (request, sender, sendResponse) {
  console.log("Foo")
})

I'm also getting this console output:

Manifest: property 'url' ignored, should be within scope of the manifest.

Manifest: property 'url' of 'shortcut' not present.