As large as 12 TB is, it is entirely possible it is insufficient for Time Machine.
The reason is that TM requires enough free space to create one complete restorable system backup, plus sufficient space to create at least one additional backup of information that has changed since the previous one, plus an additional amount of "overhead" that is not easily calculated (but a very approximate guess of 15% can be considered a minimum, and a lot more than that is possible).
In other words,
Notwithstanding this clear math (the BP disc is larger than the target disc) ...
That's not all there is to it.
.... and the fact that TM should erase the older BUs to make room for the new one,
TM only does that after successful completion of a subsequent backup. You can see it do that if you were to examine its logs. You have that backup. TM will not touch it until it creates a newer one.
The salient principle to keep in mind is that TM guarantees an absolute minimum of one and only one complete, restorable system backup. More than that is "nice to have" but not guaranteed.
Bottom line: if TM says it needs more space, then it needs more space.