This is the right perspective. It costs as much as one additional tool call in the conversation. It’s a bit weird to do it on a timer, which inflates a bit over “just a tool call”, but not by much?
Tool calls don’t sent the full transcript? I think you mean one more turn?
Pretty much everything sends the full transcript. That’s how LLMs work, and why “compact before cache expiry” is now a default in Claude Code. Cache hits are incredibly cheap to service on the provider side.