I don't know how large the cache is, but Gemini guessed that the quantized cache size for Gemini 2.5 Pro / Claude 4 with 1M context size could be 78 gigabytes. ChatGPT guessed even bigger numbers. If someone is able to deliver a more precise estimate, you're welcome to :-).

So it would probably be a quite a long transfer to perform in these cases, probably not very feasible to implement at scale.

Whats lost on this thread is these caches are in very tight supply - they are literally on the GPUs running inference. the GPUs must load all the tokens in the conversation (expensive) and then continuing the conversation can leverage the GPU cache to avoid re-loading the full context up to that point. but obviously GPUs are in super tight supply, so if a thread has been dead for a while, they need to re-use the GPU for other customers.