A Microsoft file hosting and synchronization service.
What should he do to avoid files and desktop being downloaded automatically ?
He can go to Choose Folders in OneDrive Settings > Account tab > Choose Folders, and select only the folders he wants downloaded to his PC.
https://youtu.be/QI-0geH0lsI?t=49
Sorry, but Windows users can't uncheck the system folders: Desktop, Documents, Pictures, Music, and Videos—only folders outside them. So if he wants a OneDrive backup of those folders on his new PC, he must also sync the files from the family PC.
To avoid backing up files from the family PC while still getting a full backup, I suggest he use a different account on his new PC. Microsoft 365 Family lets you add up to 6 family accounts, so he can add another account to the family group if he wants.