Not sure factory reset was successful

I am trying to wipe my data from an old MacBook Air. I followed the factory reset guide but couldn’t sign out of iCloud, iTunes etc for the initial steps. I used disk recovery to erase the disk anyway which was successful I think. Will this have now wiped all files and accounts if macOS is then reinstalled. I can’t do the install as I can’t connect to WiFi. I’m happy to hand the laptop over without installing the operating system if I can be confident that the data has been removed. I have since removed the MacBook from my ICloud on another device.thanks.