[BUG] insane cache-writes despite empty directory

I was wondering why my costs were so insane. $0.05 just to ask a question where it doesn't read anything from the filesystem.

I did a bunch of testing and found that it's very consistent even as far back as v1.0.24

Here is what i did:

1. delete ~/.claude to remove the possibility that some of those files may be cached.
2. create a new dir ~/test/
3. start Claude and ask any simple question. eg: What can you tell me about this project without looking at the filesystem or reading any files - it naturally gives a simple response.

That is all. Then exit Claude, and finding this:

Total cost:            $0.0583
Total duration (API):  38.4s
Total duration (wall): 41.8s
Total code changes:    0 lines added, 0 lines removed
Token usage by model:
    claude-3-5-haiku:  7.4k input, 265 output, 0 cache read, 0 cache write
       claude-sonnet:  3 input, 74 output, 0 cache read, 13.4k cache write

Can someone please help me understand? I accept we have system prompts, i'm not suggesting it should be zero... but this seems a little excessive no?