Erasing Mac and reinstalling macOS

Boot your Mac in Recovery mode by restarting and when you hear the startup chime press the Command-R (⌘R) keys until you see the Apple logo and progress bar. Use a wired USB keyboard for this.

• When the macOS Utilities window appears, select Disk Utility.

• Click Disk Utility > View > Show All Devices, then select the top-most drive device on the left.

• Click Erase and then set the parameters. Name the drive/volume Macintosh HD, APFS format (for Catalina or Big Sur) or Mac OS Extended (Journaled) format (for High Sierra or Mojave) and GUID partition map scheme.

• Quit DU and select Reinstall macOS.

• Follow the prompts to select the install destination drive and reinstall the OS.

How to reinstall macOS from macOS Recovery - Apple Support

How to create a bootable installer for macOS - Apple Support

That’s if you want to start over. Scorched Earth.

To be clear, the password your were prompted for was the password for your network and not your computer user password.

Being that your Mac does not appear to see a valid macOS startup volume, I'd say you've succeeded in erasing the boot drive. At this point, since you're goal is to trade the Mac in to Apple for credit, I'd say you're okay. Apple do not need a valid OS on the machine you trade in. The fact that it boots to the recovery system should be validation enough that the Mac is operational for their purpose. Whatever they have planned for the Mac as it gets recycled certainly does not include reusing whatever drive is currently in the machine.

I would be content to leave the Mac as it is working and move forward with your trade in plan.

However, if you must know a little more about the spinning globe, you can take a look at this support document –

If your Mac doesn't start up all the way - Apple Support