Using an old MacBook for Time Machine backup of new MacBook

I understand you would like to use an old MacBook as a backup storage device for Time Machine, is that correct?

A Mac's built-in storage is not one of the devices that can be used as a Time Machine backup disk: Types of disks you can use with Time Machine on Mac - Apple Support

Since a TimeMachine backup drive should be about 3 times the size of the drive that you're backing up, it seems likely that this would not be a good idea.