Random notification vibrations, but no notification after recent software update.

You might not be getting notifications on your iPhone for a few reasons. Here are some of the most common causes:

• Do Not Disturb mode is turned on. Do Not Disturb mode silences all notifications, so ensure it's turned off. You can do this by swiping down from the top of your screen and tapping the crescent moon icon.
• You're in Focus mode. Focus modes are like the Do Not Disturb mode, but they can be customized to block notifications from specific apps or people. To check if you're in Focus mode, swipe down from the top of your screen and tap the Focus icon.
• You've turned off notifications for a specific app. You can turn off notifications for individual apps in the Settings app. To do this, go to Settings > Notifications and scroll down to the app you want to change. Toggle the Allow Notifications switch to the off position.
• Your iPhone is in Airplane mode. Airplane mode turns off all wireless connections, including cellular data and Wi-Fi. This means that you won't be able to receive notifications if your iPhone is in Airplane mode.
• Your iPhone is not connected to the internet. If your iPhone is not connected to the internet, you won't be able to receive notifications from apps that need to connect to the internet to send notifications.

If you've checked all of these things and you're still not getting notifications, you can try restarting your iPhone. If that doesn't work, you can contact Apple support for help.

Have you enabled Scheduled Summary?

Settings > Notifications > [Select the App that you are having trouble receiving immediate notifications]

See the pic below for a few examples. Please select immediate delivery.

Go to Settings and tap Notifications. Select an app under Notification Style. Under Alerts, choose the alert style that you want. If you turn on Allow Notifications, choose when you want the notifications delivered — immediately or in the scheduled notification summary.

Use notifications on your iPhone, iPad, and iPod touch

Change notification settings on an iPhone

1. Go to Settings > Notifications.
2. To schedule a notifications summary, tap Scheduled Summary, then turn on Scheduled Summary. ... 
3. To choose when you want most notification previews to appear, tap Show Previews, select an option—Always, When Unlocked, or Never—then tap.

More items...

Change notification settings on iPhone - Apple Support (IN)

You can allow access to the Notification Center on the Lock Screen. Go to Settings > Face ID & Passcode (on an iPhone with Face ID) or Touch ID & Passcode (on other iPhone models). Enter your passcode. Scroll down and turn on Notification Center (below Allow Access When Locked).

View and respond to notifications on iPhone - Apple Support (IN)

Here are some additional tips for troubleshooting notification problems on your iPhone:

• Make sure that your iPhone is not in silent mode.
• Check the notification settings for individual apps to make sure that they are turned on.
• Make sure that your iPhone is connected to a Wi-Fi network or cellular data network.
• Restart your iPhone.
• Update your iPhone to the latest version of iOS.
• Contact Apple support for help.

Updating iOS on your iPhone should typically not alter the fundamental functionality of the device. It's possible that there were underlying issues before this update, which you might not have been aware of previously or might not have noticed.

In general, iOS updates are designed to enhance the user experience, improve security, and fix bugs, rather than introducing major disruptions to core features. The reported issue of the screen flickering and displaying a white screen after an update is likely caused by factors that are not explicitly mentioned in your post.

iOS updates primarily focus on improving system performance, introducing new features, fixing bugs, and enhancing security. They are designed to preserve your personal data, settings, and information intact.

During an iOS update, your device's operating system is upgraded, but your personal data, such as contacts, photos, messages, and other information, should remain unchanged. However, it's always a good practice to perform a backup of your device before any major update to ensure that your data is safely stored.

It's important to note that while an iOS update itself should not alter personal details, it's possible that certain features or settings may be adjusted or improved with the update. In such cases, you may need to review and adjust specific settings to match your preferences after the update.

Always make sure to read and understand the update details provided by Apple before proceeding with an iOS update, and follow best practices such as backing up your device to minimize any potential risks or complications.

If the issues you mentioned are indeed caused by iOS, it's likely that numerous users who have upgraded to iOS 16.6 are experiencing similar problems. However, in order for the community on this forum to provide helpful responses, it would be beneficial for you to specify the nature of the issue you are encountering. Without this information, it may be difficult for others to address your concern effectively.

With the limited information that you have provided, It is hard to even guess the problems faced by you. 

You may get faster and better responses to your query by --> Writing an effective Apple Support Commun… - Apple ...

Please re-post with detail so that someone else can help.