Hello Hannah-Browne,
Thank you for reaching out in Apple Support Communities. Pressing the side button on your iPhone 14 Plus should lock your iPhone and go to sleep. If it's powering off unexpectedly when pressing the side button, we recommend to ensure that your iPhone has the latest version of iOS 16.2 installed. This helps to provide software improvements and enhanced security updates. Here's how:
Update your iPhone or iPad wirelessly
1. Back up your device using iCloud or your computer.
2. Plug your device into power and connect to the internet with Wi-Fi.
3. Go to Settings > General, then tap Software Update.
4. If you see more than one software update option available, choose the one that you want to install.
5. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do.
That information is outlined here for reference: Update your iPhone or iPad
Once you have the latest version of iOS 16.2 installed, you can go to Settings > Face ID & Passcode. Within this section, you can configure the settings for Face ID and your passcode.
Best regards.