Does Qwen3.5 know it needs to do this because the API in question has had loads of churn and much of its training data is on obsolete versions, or do you need to prompt it? How well does it handle having an API reference with sample code in its context window?

Having an LLM use a web search tool isn't the same thing as researching a topic, IMO, because it's so ephemeral and needs constant reinforcement. LLMs aren't learning machines, they're static ones.