Hi, stephanie from Anthropic here. Thanks for the feedback! We've updated the docs to hopefully make it a little more clear but yes search results do count towards input tokens
https://docs.anthropic.com/en/docs/build-with-claude/tool-us...
https://docs.anthropic.com/en/docs/build-with-claude/tool-us...
> Web search results in the conversation are counted as input tokens on subsequent completion requests during the current turn or on subsequent conversation turns.
Yes, that's clear.