Internal HDD not showing after erasing.

Hi,

Resetting NVRAM then boot in Recovery mode could help your issue.

Reset NVRAM or PRAM on your Mac - Apple Support

How to reinstall macOS - Apple Support

If it doesn't help, you'd better make Genius Bar reservation if your local retail Apple Store is open or find opened local Apple Authorized Service Provider to install macOS on your MacBook Air there. As far as I know, it's free.

https://www.apple.com/retail/geniusbar/

Apple - Find Locations - Location Selector

You won't see an erased drive appear in the Startup Disk utility since there is no bootable OS on the drive.

Did you erase the drive as GUID partition and MacOS Extended (Journaled) for macOS up to 10.12 or by GUID partition and APFS (top option) for macOS 10.13+? How were you booted when erasing the SSD? What OS was previously installed before you erased it?

If you ended up booting into an older version of macOS 10.12 or earlier, then you won't see an APFS volume shown on the left pane of Disk Utility although you should still see the physical SSD. If your laptop has a third party NVMe SSD installed, then these older versions of macOS won't be able to see a third party NVMe SSD.

If you are booting into a macOS 10.13+ installer, then within Disk Utility click "View" and select "Show All Devices" so that the physical drive appears on the left pane of Disk Utility.

If you just installed a third party PCIe SSD, then the laptop has to already have had macOS 10.13+ installed before the NVMe SSD shows up and only macOS 10.13+ can be installed to a third party NVMe SSD.

If you don't see the physical SSD with these instructions, then either you are using a third party SSD or the SSD may be bad.

What caused you to perform a clean install?

Try running the Apple Diagnostics to see if any hardware issues are detected.