Effort level is actually controlled entirely by system prompt (as I understand it, the model is trained on that format but still), so actually this is a valid way to check I think

I know that's true for Qwen but I don't think most models work that way?

OpenAI models also work this way, as evidenced by full cache blowout when changing reasoning level. Every single open-weight model I've seen also works this way (your "reasoning_effort" argument just changes a small section of the system prompt in the chat template). I would have to see some evidence to believe Anthropic were doing anything different.