Stats: Fix tooltip flash on new sites (#95466)

client/blocks/stats-navigation/index.js

@@ -63,6 +63,7 @@ class StatsNavigation extends Component {
 		adminUrl: PropTypes.string,
 		showLock: PropTypes.bool,
 		hideModuleSettings: PropTypes.bool,
+		isNewSite: PropTypes.bool,
 	};
 
 	state = {
@@ -167,6 +168,11 @@ class StatsNavigation extends Component {
 
 		// @TODO: Add loading status of modules settings to avoid toggling modules before they are loaded.
 
+		// The isNewSite value can be null so we need to guard against that.
+		// This is semantically incorrect as we expect a boolean value.
+		// TODO: Update logic in connect() function to send only true/false value.
+		const delayTooltipPresentation = isNewSite === null || isNewSite;
+
 		return (
 			<div className={ wrapperClass }>
 				<SectionNav selectedText={ label }>
@@ -224,7 +230,9 @@ class StatsNavigation extends Component {
 							pageModules={ pageModules }
 							onToggleModule={ this.onToggleModule }
 							isTooltipShown={
-								showSettingsTooltip && ! isPageSettingsTooltipDismissed && ! isNewSite
+								showSettingsTooltip &&
+								! isPageSettingsTooltipDismissed &&
+								! delayTooltipPresentation
 							}
 							onTooltipDismiss={ this.onTooltipDismiss }
 						/>