Claude models seem to work far better in Anthropic harnesses. I don't know if this is because they are trained in that context or because they offer different models through external APIs.

Depends what you mean by "apply." The harness-specific instructions (Claude Code's own system prompt quirks) only get sent if Claude Code is the program calling the API. OpenCode or any other third-party tool writes and sends its own system prompt instead, so those exact lines aren't there. Whatever behavior shows up across different harnesses anyway is more likely a trained default of the model itself, not something coming from a particular harness's prompt.