Chrome Webstore tracks your user base. They actually track weekly users.

If you want to know daily users (DAU) the only way to measure it is including analytics to the extension.

I experiment on my own extension Email extract.

How to set up Google Analytics to measure active users

  1. Add additional file and permissions to manifest.json
...

"background": {
  "scripts": [ ... "background-analytics.js"]
  ...
},

...

"content_security_policy": "script-src 'self' https://www.google-analytics.com; object-src 'self'"

...

2. Add another background script

window.ga=window.ga||function(){(ga.q=ga.q||[]).push(arguments)};ga.l=+new Date;
ga('create', 'UA-XXXXXXX-XX', 'auto');
ga('set', 'checkProtocolTask', null);
ga('send', {'hitType':'pageview', 'page': '/background'});

(function() {
   var ga = document.createElement('script');
   ga.type = 'text/javascript';
   ga.async = true;
   ga.src = 'https://www.google-analytics.com/analytics.js';
   var s = document.getElementsByTagName('script')[0];
   s.parentNode.insertBefore(ga, s);
})();

setInterval(()=>{
   ga('send', {'hitType':'pageview', 'page': '/background'})
}, 24*60*60*1000)

3. Every time extension loaded (and every 24 hours if it's persistent) you will see  hits on "/background" page in Google Analytics account.

How to use

  1. Add a custom segment in Google Analytics
Custom segment "Extension users" in Google Analytics

2. Select this custom segment and go to Audience / Active users page. You can see DAU and weekly active users.

Daily Active Users for chrome extension

3. Want to know what is your retention? Go to Audience / Cohort analysis page

Cohort analysis for retention