The system behaviour is totally up to anthropic's discretion. Its current behaviour is verifiable. In claude code, spawn a subagent with

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

I'm pretty sure the system instructions are a function of your environment and not the same universally. That said, there should be a finite number of branches so still cacheable.