Forgive my ignorance but wouldn't a TPU be a kind of ASIC where the application is model inference? The TPU Wikipedia article also says it's an ASIC - we should update it if it's wrong.
In the limit, even a CPU could be called an ASIC because certain algorithmic operations (ALU etc) are implemented in hardware. CPU/ASIC are really poles of a gradient, with a CPU implementing very little in hardware and most in software, while an ASIC has very little software and lots of hardware. A TPU is presumably in between. I would argue however that it is closer to a GPU than to a full-blown ASIC, because the weights are stored in memory only, making them software.