fix(kiro): add SSE event: prefix for Claude client compatibility

Amp-Thread-ID: https://ampcode.com/threads/T-019b08fc-ff96-766e-a942-63dd35ed28c6
Co-authored-by: Amp <amp@ampcode.com>

internal/translator/kiro/claude/kiro_claude.go

@@ -1,10 +1,14 @@
 // Package claude provides translation between Kiro and Claude formats.
 // Since Kiro uses Claude-compatible format internally, translations are mostly pass-through.
+// However, SSE events require proper "event: <type>" prefix for Claude clients.
 package claude
 
 import (
 	"bytes"
 	"context"
+	"strings"
+
+	"github.com/tidwall/gjson"
 )
 
 // ConvertClaudeRequestToKiro converts Claude request to Kiro format.
@@ -14,8 +18,52 @@ func ConvertClaudeRequestToKiro(modelName string, inputRawJSON []byte, stream bo
 }
 
 // ConvertKiroResponseToClaude converts Kiro streaming response to Claude format.
+// It adds the required "event: <type>" prefix for SSE compliance with Claude clients.
+// Input format: "data: {\"type\":\"message_start\",...}"
+// Output format: "event: message_start\ndata: {\"type\":\"message_start\",...}"
 func ConvertKiroResponseToClaude(ctx context.Context, model string, originalRequest, request, rawResponse []byte, param *any) []string {
-	return []string{string(rawResponse)}
+	raw := string(rawResponse)
+
+	// Handle multiple data blocks (e.g., message_delta + message_stop)
+	lines := strings.Split(raw, "\n\n")
+	var results []string
+
+	for _, line := range lines {
+		line = strings.TrimSpace(line)
+		if line == "" {
+			continue
+		}
+
+		// Extract event type from JSON and add "event:" prefix
+		formatted := addEventPrefix(line)
+		if formatted != "" {
+			results = append(results, formatted)
+		}
+	}
+
+	if len(results) == 0 {
+		return []string{raw}
+	}
+
+	return results
+}
+
+// addEventPrefix extracts the event type from the data line and adds the event: prefix.
+// Input: "data: {\"type\":\"message_start\",...}"
+// Output: "event: message_start\ndata: {\"type\":\"message_start\",...}"
+func addEventPrefix(dataLine string) string {
+	if !strings.HasPrefix(dataLine, "data: ") {
+		return dataLine
+	}
+
+	jsonPart := strings.TrimPrefix(dataLine, "data: ")
+	eventType := gjson.Get(jsonPart, "type").String()
+
+	if eventType == "" {
+		return dataLine
+	}
+
+	return "event: " + eventType + "\n" + dataLine
 }
 
 // ConvertKiroResponseToClaudeNonStream converts Kiro non-streaming response to Claude format.