Apparently, the Toshiba encryption you mentioned is the reason why you get the error "Unable to write to the last block of the device. : (-69760)."
You were asked to initialize the drive because your new Mac can't read it due to its encryption. If you can plug the drive back into the old MacBook Air and decrypt the drive, your new Mac will read it just fine without the need for reformatting.
If you don't know how to decrypt the drive, ask Toshiba support for help. Or, you can try to format the external hard drive on the MacBook Air if it doesn't contain important data.
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Fix 'Unable to write to the last block of the device' 69760
