Ok, this will involve using another apple computer that already has or is compatible to run Catalina. On that other computer, open the Apple Apps Store and download the Full Catalina Installer ( about 8.4 GB in size ). Once downloaded, do NOT let it install. There should be a new application is Applications folder called Catalina Installer or something by that name. Get a USB Flash Drive with 16 GB capacity and Empty. Use Disk Utilities >> Show all Devices and point it to the USB Drive. Format it as HFS+ and GUID partition. ** will perform the task and name it Untitled , leave it that name. Now open Terminal copy and past these instruction without Quotation marks
" sudo /Applications/Install\ macOS\ Catalina.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled " . Terminal will require the password of that computer. Type it in but be aware it will be invisible. Let it do its thing. Could take 10 - 15 minutes. Once completed it will say Successful or Complete. This is a Bootable Installer of Catalina. The Catalina Installer in Application folder can be saved to external drive or deleted.
Now, on your malfunctioning MBA, boot in Internet Recovery Mode once again. Once in look along the Top for Utilities >> Security Options >> open it. There are two sections with Default options engaged. Change to first section to None. Second section Enable Booting from USB - External Drives. This will permit booting from the USB Installer that was just created.
Lastly, shutdown with the USB Installer attached. Reboot and Immediately hold Option key. Choose the USB Installer. It will load slowly. Once in Disk Utilities .>> Show All Devices and choose the Apple SSD xx and format APFS and GUID Partition. Back out of Disk Utilities and Install Catalina
