fix: dynamically update timestamps based on the chosen timezone in the Advanced Settings (#196977)

## Summary

This PR fixes the
[#190562](https://github.com/elastic/kibana/issues/190562) where the
created and updated timestamps for Dashboards do not respect the default
timezone settings in advanced settings.

Currently, if the user changes the timezone in the advanced settings,
the timestamps for the activity monitor flyout still display timestamps
from the default browser timezone. This PR ensures that the timestamps
display in the desired timezone.

![Screenshot 2024-10-19 at 13 35
00](https://github.com/user-attachments/assets/399a3b0a-d16a-4010-8560-06f3a4bcbc96)

![Screenshot 2024-10-19 at 13 36
02](https://github.com/user-attachments/assets/62a5bf2f-c5c3-474d-b810-3b1f414d2b14)

packages/content-management/content_insights/content_insights_public/src/components/activity_view.tsx

@@ -9,6 +9,7 @@
 
 import { EuiFlexGroup, EuiFlexItem, EuiPanel, EuiSpacer, EuiText } from '@elastic/eui';
 import { i18n } from '@kbn/i18n';
+import moment from 'moment-timezone';
 import { FormattedMessage } from '@kbn/i18n-react';
 import React from 'react';
 import {
@@ -97,10 +98,16 @@ export const ActivityView = ({ item }: ActivityViewProps) => {
   );
 };
 
-const dateFormatter = new Intl.DateTimeFormat(i18n.getLocale(), {
-  dateStyle: 'long',
-  timeStyle: 'short',
-});
+const formatDate = (time: string) => {
+  const locale = i18n.getLocale();
+  const timeZone = moment().tz();
+
+  return new Intl.DateTimeFormat(locale, {
+    dateStyle: 'long',
+    timeStyle: 'short',
+    timeZone,
+  }).format(new Date(time));
+};
 
 const ActivityCard = ({
   what,
@@ -130,7 +137,7 @@ const ActivityCard = ({
               id="contentManagement.contentEditor.activity.lastUpdatedByDateTime"
               defaultMessage="on {dateTime}"
               values={{
-                dateTime: dateFormatter.format(new Date(when)),
+                dateTime: formatDate(when),
               }}
             />
           </EuiText>