macOS re-installation failed. How to wipe SSD?

In theory you should be able to boot into Recovery Mode using Command + R, but this will boot to the local recovery volume if it exists, otherwise it will try to boot into Internet Recovery Mode which in theory should boot into the macOS 11.x Big Sur installer, but could equally boot into the installer for the original OS.

You can erase the physical SSD by booting into Internet Recovery Mode (Command + Option + R) for the online macOS 12.x Monterey installer. You can use Disk Utility to erase the physical SSD, but within Disk Utility you may first need to click "View" and select "Show All Devices" before the physical SSD appears on the left pane of Disk Utility. Unless you can boot into the online Big Sur installer, then this won't really benefit you since you don't have a bootable macOS 11.x Big Sur USB installer (In theory you should be able to boot Big Sur online installer, but unfortunately it does not always go as planned).

For creating a macOS USB installer... unfortunately you need access to another Qualifying Mac to create a bootable macOS USB 10.13+ USB installer. A Qualifying Mac would be one from Late-2009 to 2020 which can be used for a macOS 10.13 or 11.x USB installer (Late-2009 to 2018 for 10.13, or Late-2013 to 2020 for v11.x).

How to create a bootable installer for macOS - Apple Support

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

There are instructions for attempting to manually update the laptop's system firmware to allow macOS Monterey installer to work with a third party SSD, but it does require a system firmware level of at least 195.0.0.0.0+ IIRC (use at your own risk):

https://tinyapps.org/blog/202110270700_monterey-third-party-ssd.html

Edit: Another option is to install macOS to an external USB3 SSD. This would allow you to install the original factory OS which then would allow you access to create a bootable macOS USB installer for the desired version of macOS 10.13+.

All of those multiple volumes are from the macOS installer and is completely normal.

What is not normal is not seeing the physical SSD in the list. There are three possible reasons for this:

• SSD has failed (or Logic Board failure)
• The laptop is using a third party NVMe SSD internally and you are booting a pre-macOS 10.13 installer. Your picture of Disk Utility is showing a pre-macOS 10.13 version of the Disk Utility app.
• The laptop is using a third party NVMe M.2 SSD.... maybe the SSD adapter is bad or incompatible (same may be true for the SSD as well)

If an NVMe SSD is being used internally, then you need to boot into a macOS 10.13+ since older versions of macOS don't have the necessary NVMe driver. If you just installed a third party NVMe SSD, then did the laptop at some point in its past already have macOS 10.13+ installed? If not, then you will need to first install an Apple OEM SSD internally and install macOS 10.13+ so that the laptop's system firmware is updated to support an NVMe SSD.

FYI, when using the "diskutil list" command, add on the "internal" option so that only the internal drives and volumes are shown since all these virtual macOS installer volumes get in the way.

diskutil  list  internal

Option Command r ( Three Keyboard Combination ) with an Ethernet Cable from Computer to Router to avoid the iffy Manual input of Wifi Password.

This is Internet Recovery Mode and will connect to the Apple Servers.

1- It will present options >> Disk Utilities >> View >> View ALL attached Drives. 

2 - Choose the Upper Most Drive ( not the volumes indented and list below ).

3 - The drive normally is called Apple Media or Apple SSD - that is the drive to Erase and format as APFS with the GUID Partition Map. This applies to macOS 10.14 Mojave and above. 

4 - Once that is done >> backup out of Disk Utilities and choose install macOS. 

5 - Follow the prompts and it may automatically reboot several time. 

6 - Upon a final reboot - Setup Assist will present with the newer version of macOS.