Is there an app or option to require Face ID or passcode before turning off my iPhone X?

Any iPhone released in the last 6 years starting with the iPhone 11 is capable of using Find My even when the phone is powered off. Unfortunately that would not include an iPhone X and the use of Faraday Bags makes that point moot anyways. Find My on any device is not going to prevent theft, but the device will be totally unusable to the thief whether it is findable or not as long as Find My is turned on.

For the devices that support Find My when powered off, Find My is actually active much longer when off as once the battery dies there is no way to track it any further. So requiring Face ID to power off would actually have the opposite effect of shortening the time to find the device.

That is a common question asked by Android users, since not even the newer phones are able to be tracked when the device is turned off, so they have the option to require authentication. It is simply not needed on any iPhone made in the last 6 years for any tracking purposes.

No, and even if there were, it would serve no purpose other than to make basic troubleshooting impossible.

Thieves often use faraday bags to prevent devices from being able to communicate with the cellular network.

This is never going to happen. For one, if your phone locks up you would not be able to power cycle the phone to get it working again if the screen was frozen and you needed to input a password.