where can I find the There's a problem with the [your device name] that requires it to be updated or restored message

That message can arise spontaneously, or can be triggered by the reset sequence.

If you are trying to reset the device, see the following, then contact Apple using the Get Support link in the upper right of this webpage, and discuss your options and alternatives directly with Apple.

If you see the Restore screen on your iPhone, iPad, or iPod touch - Apple Support

iOS update and restore errors - Apple Support

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support