Why is my iPhone 14 Pro stuck on Silent mode?

Open the Control Center by dragging down from the battery icon and look at the button circled in green (the Do Not Disturb button). if it is white then DND is active. Tap on it to turn it off.

Are you referring to Silent Mode, the physical switch on the side of your iPhone or Do Not Disturb/Focus?

If you are referring to Do Not Disturb/Focus, it can turn on automatically if you have a schedule or Smart Activation in place. You can turn those off by going to Settings > Focus > Do Not Disturb > Delete any associated schedules.

If the physical Silent Mode switch is not working and switching by itself , that is usually indicative of a hardware/physical issue. There may also be some debris or something lodged in it. Don't try to fiddle with it. As a result, I suggest you have your iPhone taken a look at your nearest Apple Store Genius Bar or Apple Authorized Service Provider.

Genius Bar Reservation and Apple Support Options - Apple