disk0 is the Physical built-in internal drive of size 500 GB. it has an EFI partition, so it is getting ready to be a bootable drive. But it has No APFS additional file structures, and has no MacOS Volumes AT ALL.
macOS only can install on a proper Volume, and you are not showing one there.
disk1 is the usual "macOS Base System" (disk Image) of size 2 GB -- likely the recovery software from the Mac's ROM.
The additional about 25 untitled disks of very small sizes are created by Recovery when starting up, so that the Internal drive can be COMPLETELY free to be properly initialized.
You need to invoke disk Utility, and change the little View menu to "show all devices'
then select the PHYSICAL device, by its immutable, manufacturer-given device-name.
then ERASE the PHYSICAL device and create a Mac volume in the process.
NO your files are NOT recoverable after an ERASE -- they are already gone. That is why Apple has been nagging you to create a Time Machine backup on another drive.
Shaw All Devices view:
