How do I disable Apple Intelligence timer on iPhone 16 silence button?

You might want to see this instructions on how to put the action button back to the function of silencing your phone

Customize the Action button

1. On supported models, go to Settings  > Action Button.
2. An image of the side of the iPhone appears with icons representing actions you can assign to the Action button.
3. 
   
4. To choose an action, swipe to the action you want to use—its name appears below the dots.
5. Tip: To customize the Action button to put iPhone in Silent mode, swipe to . To choose another action, swipe to it.
6. If there are additional options for the selected action,  appears below the action; tap it to see the list of options.
7. For the Controls, Shortcut, and Accessibility actions, you need to tap the button below the action and select a specific option—otherwise the Action button does nothing.