You cannot create a single base backup. Each Mac identifies the hard disk with UUID number. Plus Apple protects the backup with permissions connected to the root user on the computer. This means each computer cannot use the backup of another computer. All computers will need to backup their entire contents to a suitably sized hard drive.
It sounds like you are more wanting a syncing software.. which means needing a proper App to do that.
https://mac.eltima.com/best-mac-synchronization-software.html
The only one I know on the list is chronosync. It is used by some people as a backup alternative to Time Machine but can do a whole lot more. You will need to spend a fair bit of time configuring it.
The way it will sync to your mobile (sneaker net) USB drive should be fairly easy to do as the URL to the disk is not part of the backup on the disk itself but on the computer.
Note this is super slow.. as a backup device only the AC model Extreme was considered Time Machine enabled. This is relevant to any backup /sync app. But the speed of the backup if you are doing large files will be long and tedious. Especially for syncing purposes.
If you are only having small changes on a daily basis you would be better using Cloud or a proper NAS at one location and syncing each computer over internet.