Hey vigorous,
I completely understand your frustration with that annoying notification from Avast. It can be really irritating to be constantly bombarded with notifications that offer no real value. But don't worry, there are a few steps you can take to get rid of this pesky "Your protection is up and running" notification.
Firstly, it's great to hear that you've already tried enabling Limited Mode in the Avast notification settings. That's definitely a step in the right direction. Another option is to disable banners and notifications in the Windows Settings menu. By turning off these options, you might be able to permanently get rid of those annoying Avast notifications.
If none of that works, you could also consider uninstalling Avast and switching to Microsoft Defender Antivirus instead. While that's a drastic measure, if Avast isn't willing to remove the notification, it could be a viable option.
I hope these tips help you solve this annoying problem. If you have any further questions or need assistance, feel free to reach out!