iCloud Erorr

So I was testing my old MacBook and to wanted to add my Apple ID and when It send a code to my iPhone 14 Pro it sent the code but I looked back at the Mac and I didint see a type-in part I contacted Apple support they didint help I contacted my friend who is a mac user for 3 years he didint really help he said try reinstalling macos but I didint wanna lose my data cause if I use Time Machine then it will restore the problem so I just decided to ask Apple community for help