iPhone buzzing at night with Do Not Disturb enabled

You have not provided any screenshots of the Sleep Schedule:

If you haven’t set up a Sleep Schedule—or if you haven’t selected the specific days when you want it to apply—your iPhone won’t automatically enable Sleep Focus. That means on nights without a defined schedule, your device may still send notifications or buzz, since Sleep Focus only activates when a schedule is in place and properly configured. To ensure uninterrupted rest, it’s important to create a Sleep Schedule and assign it to the nights you don’t want to be disturbed.

Tap Sleep, scroll down to Your Schedule, then tap Sleep Schedule. Turn on Sleep Schedule, tap Set Your First Schedule, then do the following:.Read more

Set up a sleep schedule in Health on iPhone

This happened to me last night (WhatsApp notifications) and it’s only when I went into the health centre to delete and recreate my sleep schedule I realised the option to link it to sleep focus was off. Check to see if yours is toggled on.

Delete the current Sleep Focus and create a new one.

Important government alerts will still reach you, even if Do Not Disturb or Sleep Focus is on.

Which is buzzing (Calls/Texts) is not clear from your post.

What Call? On an iPhone, you can make and receive various types of calls. Here are the different types:

1. These are standard voice calls made over the cellular network. They utilize your carrier's voice network to connect you with other phone numbers. Allow phone calls on your iPad, iPod touch, and Mac
2. FaceTime Audio allows you to make voice calls over Wi-Fi or cellular data using your internet connection. It provides higher audio quality compared to traditional cellular calls.
3. FaceTime Video enables you to have video calls with other FaceTime users. It uses the front or rear camera on your iPhone to transmit live video during the call. Use FaceTime with your iPhone or iPad - Apple Support (IN)
4. VoIP (Voice over Internet Protocol) calls use internet connectivity to make phone calls. Apps like Skype, WhatsApp, Viber, and Google Hangouts utilize this technology, allowing you to make voice and video calls over the Internet.
5. Some carriers support Wi-Fi calling, which allows you to make and receive calls over a Wi-Fi network instead of relying solely on cellular coverage. This can be useful in areas with weak cellular reception. Make a call with Wi-Fi Calling - Apple Support (IN)
6. The App Store offers numerous calling apps that utilize different technologies. These apps can provide additional features and options for making calls, such as international calling, call recording, and more.

It's important to note that the availability of certain call types may depend on your iPhone model, iOS version, and carrier.

Text messages on iPhone can come in various formats and types, each with its features and purposes:

1. Apple Platform (iPhone , iPad, and Mac)
   1. iMessage: This is Apple's proprietary messaging service, available only between Apple devices. iMessages are sent over Wi-Fi or cellular data, rather than traditional SMS networks. iMessage offers enhanced features such as read receipts, typing indicators, multimedia support (photos, videos, etc.), and end-to-end encryption for privacy. These messages appear in blue bubbles in the Messages app.
2. Carrier (Cellular Service Provider)
   1. SMS (Short Message Service): SMS is the traditional text message format used on all mobile phones. It is limited to 160 characters and is sent over the cellular network. SMS does not require an internet connection, but it also lacks features like media sharing or real-time typing indicators. Messages sent via SMS appear in green bubbles on an iPhone.
   2. MMS (Multimedia Messaging Service): MMS allows users to send multimedia content, like images, videos, and audio, along with text messages. Unlike SMS, MMS requires a data connection. MMS messages also appear in green bubbles on iPhones, as they are sent over the cellular network instead of Apple's iMessage system.
   3. RCS (Rich Communication Services): RCS is a modern messaging protocol designed to replace SMS and MMS, offering features similar to iMessage, such as high-quality media sharing, read receipts, typing indicators, and more. It is supported by some Android phones and mobile carriers, though not yet universally available. RCS can be used in messaging apps that support it, but it is not natively integrated into Apple's Messages app at the moment.
3. Third-Party Text Messaging Apps: Apart from iMessage, iPhone users can install and use various third-party messaging apps such as WhatsApp, Facebook Messenger, Telegram, Signal, and more. These apps typically use internet connections (Wi-Fi or data) to send messages and offer additional features like voice and video calls, group chats, file sharing, and security features (like end-to-end encryption). These messages are usually separate from iMessages and are managed within their own app.

Each of these types of messages may have different behaviors, settings, and limitations depending on the network, device, or app being used.