Chore: Logging improvements (#44925) (#44996)

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

(cherry picked from commit 05ea825c76)

Co-authored-by: Marcus Efraimsson <marcus.efraimsson@gmail.com>

pkg/services/login/loginservice/loginservice_test.go

@@ -46,7 +46,7 @@ func Test_syncOrgRoles_doesNotBreakWhenTryingToRemoveLastOrgAdmin(t *testing.T)
 
 func Test_syncOrgRoles_whenTryingToRemoveLastOrgLogsError(t *testing.T) {
 	buf := &bytes.Buffer{}
-	logger.SetLogger(level.NewFilter(log.NewLogfmtLogger(buf), level.AllowInfo()))
+	logger.Swap(level.NewFilter(log.NewLogfmtLogger(buf), level.AllowInfo()))
 
 	user := createSimpleUser()
 	externalUser := createSimpleExternalUser()