I have a old MacBook Pro and a new MacBook Pro i want to know if it possible to make a time machine backup of the new mac but use the old macs drive via target disk mode so that way i dont have to buy an external drive (the new Mac is on macOS Ventura and the old Mac is on macOS Catalina)
MacBook Pro
You can use any drive, even one that is not as large as the recommendation. after a while, it may become annoying, but that could be some time from now.
In re-reading, I see that the steps for a Shared time machine backup destination presumed you were using your network, and keeping both Macs as separate MacOS devices. if you want to put the old Mac in target disk mode, it becomes a LOCAL drive, and there is no setup, you just use it. Support for target disk mode is in the old computer's ROM, you don't use MacOS.
Transfer files between two Mac computers using target disk mode - Apple Support
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The recommended size of an external drive for time machine is at least 2.5 times the size of what needs to be backed up, for long-term trouble-free operation.
¿do you have that much space on the old one?
If you do, and the old Mac is running at least 10.13 Sierra, you can set up File Sharing, then designate the shared Folder as Shared Time Machine destination. You need to follow the slightly convoluted procedure exactly:
Back up to a shared folder with Time Machine on Mac - Apple Support
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My new Mac is 256 GB and my old one is 750 GB
Time Machine and Target Disk Mode
