Avoid double printing INFO deprecation messages

Fixes #11645

hugolib/integrationtest_builder.go

@@ -394,10 +394,10 @@ func (s *IntegrationTestBuilder) initBuilder() error {
 
 		logger := loggers.New(
 			loggers.Options{
-				Stdout:   w,
-				Stderr:   w,
-				Level:    s.Cfg.LogLevel,
-				Distinct: true,
+				Stdout:        w,
+				Stderr:        w,
+				Level:         s.Cfg.LogLevel,
+				DistinctLevel: logg.LevelWarn,
 			},
 		)
 

hugolib/site_new.go

@@ -117,7 +117,7 @@ func NewHugoSites(cfg deps.DepsCfg) (*HugoSites, error) {
 
 		logOpts := loggers.Options{
 			Level:              cfg.LogLevel,
-			Distinct:           true, // This will drop duplicate log warning and errors.
+			DistinctLevel:      logg.LevelWarn, // This will drop duplicate log warning and errors.
 			HandlerPost:        logHookLast,
 			Stdout:             cfg.LogOut,
 			Stderr:             cfg.LogOut,