Clean install on MacBook Air 2014 gone wrong, I cannot install a new version of OS?

The solution is to boot macOS Recovery again and use Disk Utility to completely erase the device.

Follow these instructions: Erase and reformat a storage device in Disk Utility on Mac - Apple Support.

Pay attention to Steps 3 and 4: Be sure to choose View > Show All Devices. The "Device" in its context refers to the entire storage device, meaning not a volume or partition subordinate to that device. For the file system format (Step 6) select Mac OS Extended (Journaled).

Then, you can reinstall macOS.

Does this laptop use a third party NVMe SSD? If so, then you need to boot into a macOS 10.13+ installer. Try using Command + Option + R to access Internet Recovery Mode for the online macOS 11.x Big Sur installer. Unfortunately with some Macs no matter the keys used to access recovery mode it will result in the installer for the OS which originally shipped with the Mac from the factory.

You can install macOS 10.9 Mavericks to an external drive so you can get access to the Big Sur installer which you can then use to install Big Sur onto the internal SSD. You can also create a bootable macOS USB installer using the instructions in this Apple article (requires booting Mavericks to an external drive, or access to another Qualifying Mac):

Create a bootable installer for macOS - Apple Support

If you have an original Apple SSD installed internally, then you may need to use Disk Utility to partition & format the whole physical SSD by using the instructions in this article since earlier versions of macOS may not recognize the disk layout used by macOS 10.13+:

https://eshop.macsales.com/tech_center/formatting/Mac_Formatting_6-10_R3.pdf