Why is Time Machine reporting insufficient free space?

<< I have been monitoring the backup using for the disc utility tools. >>

Be sure you have used the tiny View menu to 'Show all devices".

From the 'Info' screen you posted, it appears you limited the Volume size to 79 GB when the Volume was created. There is no such limit built into MacOS anywhere. However, if the factory created a 79 GB Volume for testing, and you JUST erased by Volume, it may have created a new Volume the same size as the pre-existing Volume.

It is not clear whether you could use the 'Partition' tool in disk Utility to increase the size that dramatically. Because there is so much risk involved in changing partition sizes, it may be better to simply erase the DEVICE again -- taking Great care to erase it by Device, using the immutable manufacturer-given device-name. Otherwise you way simply just erase and re-create a volume the SAME size limited size as before.

What is the exact make & model of this drive & where did you purchase it?

Is this drive an SSD or a hard drive?

Run the following command in the Terminal app and post the output here so we can get a better look at the drive layout since the Disk Utility GUI can hide details. Make sure only this one external drive is connected so that we don't have to filter out other drives:

diskutil  list  external

when showing any component, the number in the box at the TOP is the total capacity of the ENTIRE Device. On slightly older versions the words, "shared by five Volumes" used to appear.

The size of the Volume is not indicated directly in the graphical displays. You would have to add up the pieces shown, and yours show about 78 GB, as you said.

The entire Device has 16 TB capacity.

The Volume was created FAR smaller than you expected.

<< Time Machine complains there is not enough free space. >>

That message tells you WHAT DRIVE is short of space.

Sometimes the complaint is about the Source drive, where the links for the next backup are collected in a snapshot. Not enough room for the snapshot make it very hard to create the next proposed backup.