Silent mode missing on iPhone 15

On the left upper side of your iPhone, you will see the silent switch. Flip that and the iPhone will enter silent mode

BTW, if your phone has a silent switch (15 and older) it doesnt have the control centre controls.

If it has an action button (15 Pro or later) it does

Silence iPhone – Apple Support (UK)

Add a control to the Action button

You can assign a Control Center control to the Action button, and then turn the control on or off just by using the Action button.

1. Go to Settings  > Action Button.
2. Swipe to the Controls action, then tap Choose a Control.
3. Scroll through the controls or search for the control you want by entering it in the search field above the controls.
4. Tap the control you want to add.
5. For example, you can assign Dark Mode to the Action button by tapping . Then you can turn Dark Mode on or off by pressing and holding the Action button.

• On supported models, go to Settings  > Action Button. --> Use and customize the Action button on iPhone - Apple Support (IN)

Please refer to the accompanying image, which illustrates the functionality of the Silent switch on an iPhone 12 Pro. The Silent switch enables users to disable the device’s sound output, while the Control Centre provides alternative methods for controlling the device’s audio output.

Check this, first.