Fix superfluous writing header after flush in otelhttp

CHANGELOG.md

@@ -18,6 +18,7 @@ This project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.htm
 
 ### Fixed
 
+- Superfluous call to `WriteHeader` when flushing after setting a status code in `go.opentelemetry.io/contrib/instrumentation/net/http/otelhttp`. (#6074)
 - Superfluous call to `WriteHeader` when writing the response body after setting a status code in `go.opentelemetry.io/contrib/instrumentation/net/http/otelhttp`. (#6055)
 
 <!-- Released section -->

instrumentation/net/http/otelhttp/internal/request/resp_writer_wrapper.go

@@ -82,7 +82,12 @@ func (w *RespWriterWrapper) writeHeader(statusCode int) {
 
 // Flush implements [http.Flusher].
 func (w *RespWriterWrapper) Flush() {
-	w.WriteHeader(http.StatusOK)
+	w.mu.Lock()
+	defer w.mu.Unlock()
+
+	if !w.wroteHeader {
+		w.writeHeader(http.StatusOK)
+	}
 
 	if f, ok := w.ResponseWriter.(http.Flusher); ok {
 		f.Flush()

instrumentation/net/http/otelhttp/test/handler_test.go

@@ -215,6 +215,12 @@ func (rw *respWriteHeaderCounter) WriteHeader(statusCode int) {
 	rw.ResponseWriter.WriteHeader(statusCode)
 }
 
+func (rw *respWriteHeaderCounter) Flush() {
+	if f, ok := rw.ResponseWriter.(http.Flusher); ok {
+		f.Flush()
+	}
+}
+
 func TestHandlerPropagateWriteHeaderCalls(t *testing.T) {
 	testCases := []struct {
 		name                 string
@@ -265,6 +271,23 @@ func TestHandlerPropagateWriteHeaderCalls(t *testing.T) {
 			},
 			expectHeadersWritten: []int{http.StatusBadRequest},
 		},
+		{
+			name: "When writing the header indirectly through flush",
+			handler: func(w http.ResponseWriter, r *http.Request) {
+				f := w.(http.Flusher)
+				f.Flush()
+			},
+			expectHeadersWritten: []int{http.StatusOK},
+		},
+		{
+			name: "With a header already written when flushing",
+			handler: func(w http.ResponseWriter, r *http.Request) {
+				w.WriteHeader(http.StatusBadRequest)
+				f := w.(http.Flusher)
+				f.Flush()
+			},
+			expectHeadersWritten: []int{http.StatusBadRequest},
+		},
 	}
 
 	for _, tc := range testCases {