at some point some researchers were begging for GPUs... mainly for sparse work. I think that's why sparsecore was added to TPU (https://cloud.google.com/tpu/docs/system-architecture-tpu-vm...) in v4. I think at this point with their tech turnaround time they can catch up as competitors add new features and researchers want to use them.
Mostly embedding, but IIRC DeepMind RL made use of sparsity- basically, huge matrices with only a few non-zero elements.
BarnaCore existed and was used, but was tailored mostly for embeddings. BTW, IIRC they were called that because they were added "like a barnacle hanging off the side".
The evolution of TPU has been interesting to watch; I came from the HPC and supercomputing space, and seeing Google as mostly-CPU for the longest time, and then finally learning how to build "supercomputers" over a decade+ (gradually adding many features that classical supercomputers have long had), was a very interesting process. Some very expensive mistakes along the way. But now they've paid down almost all the expensive up-front costs and can now ride on the margins, adding new bits and pieces while increasing the clocks and capacities on a cadence.