chore(otelgin): refine error recording in gintrace

instrumentation/github.com/gin-gonic/gin/otelgin/gintrace.go

@@ -6,7 +6,6 @@
 package otelgin // import "go.opentelemetry.io/contrib/instrumentation/github.com/gin-gonic/gin/otelgin"
 
 import (
-	"errors"
 	"fmt"
 
 	"github.com/gin-gonic/gin"
@@ -97,7 +96,9 @@ func Middleware(service string, opts ...Option) gin.HandlerFunc {
 			span.SetAttributes(semconv.HTTPStatusCode(status))
 		}
 		if len(c.Errors) > 0 {
-			span.RecordError(errors.New(c.Errors.String()))
+			for _, err := range c.Errors {
+				span.RecordError(err.Err)
+			}
 		}
 	}
 }

instrumentation/github.com/gin-gonic/gin/otelgin/test/gintrace_test.go

@@ -105,7 +105,8 @@ func TestError(t *testing.T) {
 	// configure a handler that returns an error and 5xx status
 	// code
 	router.GET("/server_err", func(c *gin.Context) {
-		_ = c.AbortWithError(http.StatusInternalServerError, errors.New("oh no"))
+		_ = c.Error(errors.New("oh no one"))
+		_ = c.AbortWithError(http.StatusInternalServerError, errors.New("oh no two"))
 	})
 	r := httptest.NewRequest("GET", "/server_err", nil)
 	w := httptest.NewRecorder()
@@ -124,10 +125,14 @@ func TestError(t *testing.T) {
 
 	// verify the error event
 	events := span.Events()
-	assert.Len(t, events, 1)
+	assert.Len(t, events, 2)
 	assert.Equal(t, "exception", events[0].Name)
 	assert.Contains(t, events[0].Attributes, attribute.String("exception.type", "*errors.errorString"))
-	assert.Contains(t, events[0].Attributes, attribute.String("exception.message", "Error #01: oh no\n"))
+	assert.Contains(t, events[0].Attributes, attribute.String("exception.message", "oh no one"))
+	assert.Equal(t, "exception", events[1].Name)
+	assert.Contains(t, events[1].Attributes, attribute.String("exception.type", "*errors.errorString"))
+	assert.Contains(t, events[1].Attributes, attribute.String("exception.message", "oh no two"))
+
 	// server errors set the status
 	assert.Equal(t, codes.Error, span.Status().Code)
 }