Google Chrome Extension chrome.browserAction.setIcon not working

I want the icon to change from one image to another (basically have the color change depending on the presence of a link on the page).

content.js

// Get all the links on the page
var links = document.getElementsByTagName("a");

// Loop through the links and look for a LinkedIn link
for (var i = 0; i < links.length; i++) {
  var link = links[i];
  if (link.href.indexOf("linkedin.com") !== -1) {
    // Found a LinkedIn link, do something with it
    console.log(link.href);
    //change color of LinkedIn button
    chrome.browserAction.setIcon({
      path : "present128.png",
    })
  }
}

manifest.json

{
  "manifest_version": 3,
  "name": "LinkedIn Link Finder",
  "version": "1.0",
  "description": "Finds a LinkedIn link on the current webpage.",
  "action": {
    "default_icon": {              
      "128": "notpresent128.png"    
    },
    "default_title": "Click Me",
    "default_popup": "popup.html"
  },
  "content_scripts": [
    {
      "matches": ["http://*/*", "https://*/*"],
      "js": ["content.js"]
    }
  ]
}

What am I missing here?

Looked into the docs for different solutions. Tried manifest V2 - tried switching images so can get the default image to start off as a different image, but cant get it to switch.

Please try this.

manifest.json

{
  "manifest_version": 3,
  "name": "LinkedIn Link Finder",
  "version": "1.0",
  "action": {
    "default_icon": {
      "128": "notpresent128.png"
    }
  },
  "content_scripts": [
    {
      "matches": [
        "<all_urls>"
      ],
      "js": [
        "content.js"
      ]
    }
  ],
  "background": {
    "service_worker": "background.js"
  }
}

contens.js

var links = document.getElementsByTagName("a");

for (var i = 0; i < links.length; i++) {
  var link = links[i];
  if (link.href.indexOf("linkedin.com") !== -1) {
    console.log(link.href);
    chrome.runtime.sendMessage({});
  }
}

background.js

chrome.runtime.onMessage.addListener(() => {
  chrome.action.setIcon({
    path: "present128.png",
  })
});