Resetting disk

You are booted into a macOS 10.13+ installer, so the OS will require the destination to be erased as GUID partition and APFS (top option). Within Disk Utility click "View" and select "Show All Devices" so the physical drive appears on the left pane of Disk Utility. Make sure to select the whole physical SSD to erase. This will be the top most item identified by its make & model.....something like "Apple SSD AP025....". This only applies to Intel Macs, don't erase the whole physical internal SSD on an Apple Silicon Mac.

The other option is to follow Apple's instructions to "erase the disk" which has the user erasing the whole "Volume Group" when erasing a disk used by macOS 10.15+. It looks like you already modified the volume group so it doesn't appear properly now, so I would recommend following my first set of instructions to erase the whole physical SSD.

With a 2018+ Mac, another option is to perform a firmware "Restore" which will reset the security enclave as well as properly erasing the internal SSD. With Intel Macs you will then need to boot into Internet Recovery Mode to reinstall macOS. Unfortunately the firmware "Restore" requires access to another Mac running macOS 12.4+ (at least the last time I checked....unfortunately this OS requirement is likely to increase in the future).

Revive or restore an Intel-based Mac using Apple Configurator - Apple Support

Revive or restore a Mac with Apple silicon using Apple Configurator - Apple Support

The APFS stuff is a disk format name. Apple File System. You don't have to use APFS but you must choose one of the format types depending on the planned usage of the disk.

What does "redownload a new disc..." mean? You don't download disks (Hard Disk Drives and Solid State Drives) as they are physical items. What exactly are you trying to do and why? For example, "Reset my Mac", "prepare the Mac for resale", "wipe the drive and reinstall the OS".

It looks like you have a 2018+ model judging by the power button and lack of a aluminum Display Bezel, most likely an Intel model, but I cannot be sure. If you cannot reinstall macOS through recovery mode, then you will need to "Restore" the firmware which will reset the security enclave & system firmware. On Apple Silicon Macs it will also push a clean copy of macOS onto the internal SSD, but with an Intel Mac you will most likely need to use Internet Recovery Mode (Command + Option + R) to reinstall macOS (hopefully it works now that the T2 chip & firmware have been reset).

Here are two Apple articles with instructions for performing a firmware "Restore" (you need to choose the correct one for your type of MBAir......Intel CPU or Apple Silicon M1/M2 CPU:

Revive or restore an Intel-based Mac using Apple Configurator - Apple Support

Revive or restore an Intel-based Mac using Apple Configurator - Apple Support

Keep in mind a "Restore" will destroy all data on the internal SSD.

If you don't know whether you have an Intel or Apple Silicon M1/M2 Mac, then enter the system serial number here:

Check Your Service and Support Coverage - Apple Support