"Input" in Claude Code

Hello ! I noticed that when I use Claude Code with an input of 100+ tokens, plus CLAUDE.md, skills, etc., and then type /usage, I see a very small number of tokens under “input”, sometimes around 10 tokens, while “cache write” is always very high. I don’t really understand how that works. Is this a different type of caching from the usual KV cache? Normally, my full request should count as input and be processed during the prefill phase in parallel. I’m asking because I have a tool that’s meant to reduce the context given to my agent. I can see that it reduces cache writes, but sometimes it doesn’t reduce the input token count, so those numbers seem a bit suspicious to me.