You can download the Android app on F-Droid if you have Izzysoft’s F-Droid repo enabled. I recommend Firefox but it’s also available for Chrome. The official website listing other instances is it xbrowsersync.org and the source code is at xbrowsersync/api on GitHub.
To use the app or addon with my instance, you’ll need to go to the settings prior to syncing anything. On desktop, open the addon, click the cog icon, and change the service URL to https://xsync.nixnet.services. You can then go back to the main screen and set it up with. In the Android app, do the same. Once you have that set, you can go back to desktop and click your user ID; it’ll display a QR code that autofills the ID field so you don’t have to type it in or copy/paste between devices. As the addon instructions say, you’ll need to disable Firefox Sync or whatever Chrome has because it can cause a lot of issues.
You can go to xsync.nixnet.services to view the status of my instance and API information.