fix(ai): expose provider response ids on assistant messages fixes #2245

packages/ai/src/providers/anthropic.ts

@@ -264,6 +264,7 @@ export const streamAnthropic: StreamFunction<"anthropic-messages", AnthropicOpti
 
 			for await (const event of anthropicStream) {
 				if (event.type === "message_start") {
+					output.responseId = event.message.id;
 					// Capture initial token usage from message_start event
 					// This ensures we have input token counts even if the stream is aborted early
 					output.usage.input = event.message.usage.input_tokens || 0;