No, as Upfort Shield is not a computer application - meaning no modifications are being made to your computer itself - it's limited to the browser where the extension is installed.
You can utilize the Browser Firewall on multiple browsers, but you'll need to make sure they are both installed and activated individually. For example, if you utilize Google Chrome and Microsoft Edge, it's necessary to install and log in to the browser extension on both browsers.
Check out the different browser extensions here: Edge, Firefox, and Chrome.