You could probably engineer your own harness or workflow to warm the cache by running a single warmup agent, but this is not at all how the tools behave out of the box. It's mostly a cost optimizaiton, so Anthropic really don't have any incentive to do it proactively, and if they did, surely they would want to tell their customers how much they were saving?
I say this as I don't actually know how Clade Code does this, since it's not open source, but I fail to see why two agents doing the same thing launched at different times would have different tools and system prompts.
If you make a bunch of identical API calls quickly, before the initial request completes its cache write, you will have cache misses.
If you make a single API call to warm the cache, then make a bunch of subsequent identical requests, you will have cache hits.
The optimization for this sort of thing is to deduplicate in-flight requests, but i've seen no evidence that is being done; the better design pattern would be an api or tool call that explicitly launches multiple agents after a shared prompt processing stage
1. Agent("Test")
2. look at your token usage
3. Repeat a few times
I didn't check again as I type this message but am somewhat sure subagent doesn't cache system prompt as of maybe last week