Chore: Logging improvements (#44925)

Fixing a couple bugs, adds some tests and hopefully decrease 
lock contention when logging.
Switching from using sync.RWMutex to go-kit SwapLogger.
Fixes bug when creating a new logger from an existing one that 
screwed up the keyvals and/or lost the logger name. 

Ref #44681

pkg/server/server.go

@@ -152,16 +152,16 @@ func (s *Server) Run() error {
 				return s.context.Err()
 			default:
 			}
-			s.log.Debug("Starting background service " + serviceName)
+			s.log.Debug("Starting background service", "service", serviceName)
 			err := service.Run(s.context)
 			// Do not return context.Canceled error since errgroup.Group only
 			// returns the first error to the caller - thus we can miss a more
 			// interesting error.
 			if err != nil && !errors.Is(err, context.Canceled) {
-				s.log.Error("Stopped background service "+serviceName, "reason", err)
+				s.log.Error("Stopped background service", "service", serviceName, "reason", err)
 				return fmt.Errorf("%s run error: %w", serviceName, err)
 			}
-			s.log.Debug("Stopped background service "+serviceName, "reason", err)
+			s.log.Debug("Stopped background service", "service", serviceName, "reason", err)
 			return nil
 		})
 	}