Backup problem

You'll need to restart your Mac in Recovery mode.

Start up your Intel-based Mac in macOS Recovery

1. Restart your Mac.
2. Immediately press and hold one of the following key combinations until you see the startup screen:

• • Command-R: Start up from the built-in macOS Recovery System. Use this key combination to reinstall the latest macOS that was installed on your system, or to use the other apps in macOS Recovery.
  • Option-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall macOS and upgrade to the latest version of macOS that’s compatible with your Mac.
  • Option-Shift-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall the version of macOS that came with your Mac or the closest version that’s still available.

Once you have restarted the Mac in Recovery, you'll now need to select Reinstall macOS and reinstall the OS on the internal startup drive. It's usually named "Macintosh HD" but the name could be something else if it was changed previously.

Make sure after you have booted into Recovery that your Mac is connected to the internet. Click the wi-fi icon at the top right of the screen to confirm or connect if necessary. Even better, connect your Mac to your router with an ethernet cable; it'll be a better connection than wi-fi.

If Apple's recovery server is unavailable, then you will have to find a way to download a macOS installer and then create a bootable installer on a USB drive.

Create a bootable installer for macOS - Apple Support

macOS installers can be downloaded by following the appropriate link found here:

How to download and install macOS - Apple Support

Creating a bootable USB installer will require that you have access to another working Mac that is able to run the OS you want to install on the problem Mac. By that I mean if you want to install macOS 11 Big Sur on the laptop, you'll need to create the bootable installer using another Mac that can run Big Sur.

Press and hold only Command-R (⌘R) at startup and see if the Mac will boot to Recovery.

If so, then you can use Disk Utility to partition the drive and create the Macintosh HD volume before you can reinstall the OS. Partition the drive with the Mac OS Extended format and the GUID partition scheme. Name the drive Macintosh HD.

Erase and reinstall macOS - Apple Support

After you have formatted the drive, you can quit Disk Utility and Launch Reinstall macOS to install a fresh copy of the OS on to the drive.

If this does not work, then I suggest you make an appointment at your nearest Apple service provider and have them evaluate the computer and reinstall macOS.

Contact Apple for support and service - Apple Support