There's no single call that can launch multiple event loops at the same time, so there really isn't a notion of serial or parallel; it's always going to be a simple question of how the first model calls made by each hit the backend. I highly doubt that a bunch of agents created within milliseconds of each other are going to get cache hits. It's more likely they will spin up in parallel. I strongly suspect if Anthropic were trying to deduplicate their inflight requests for cache efficiency, they'd at least want to tell you about it.
The system prompt and available tools would likely only change for different agent types. So how they're launched probably doesn't matter.
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.
I think you are right and most people here are overthinking it.
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