Time Machine won't recognize Seagate 2TB portable drive

Do you still need to back up those other Macs to this drive? If not, and you don't need them anymore, you could delete them.

Yes, in theory, TM will remove outdated backups, but that doesn't always happen in practice ... especially, if you use something like Parallels on your Mac. If you do, everytime you access a VM, TM will have to back up that VM. These VMs are typically many GBs in size. Of course, if you don't use a Virtual Machine manager, you can ignore this comment.

The other thing to note, is that TM will first create a local snapshot of your Mac's entire drive on that drive BEFORE sending it to the backup drive. If there is not enough space on your Mac's internal drive (80GBs would be an example) the backup will fail warning you that there is not enough space. In this case, it's not the external, but internal drive, that doesn't have enough space.

Applesup20jan20 wrote:

Is it possible to tell TM to not backup some files so that the image it needs to create on the internal drive is smaller?

Unfortunately, no. TM will always fully back up the APFS Data container to the internal drive, even if you exclude files/folders in the TM interface. It only retains them for a short period of time and thins them sooner if that internal drive has limited space. You can see these as local snapshots in the Disk Utility.

One option would be to erase the current ones, and then, run a manual TM backup to see if it succeeds.

Yes, both methods would be the means to increase the internal drive's free space. Deleting the snapshots would be the quicker of the two.

Is this 2TB external drive dedicated to Time Machine (TM) or are you using it to also store files?

This issue may also be that your Mac's internal drive does not have enough storage space to run TM properly. Please check and let us know what the remaining free space is.