In almost every reported instance, the phone would begin to charge normally once it had been unlocked and interacted with, indicating that the issue lay in the device's inactivity, and not the display's sleep status.
Thankfully, Apple's new iOS 12.0.1 update has now been released, addressing the issue with a 104MB download that "fixes an issue where some iPhone XS devices did not immediately charge when connected to a Lightning cable".
Alongside the charging bug, the firmware update is said to resolve "an issue that could cause iPhone XS devices to rejoin a Wi-Fi network at 2.4GHz instead of 5GHz," while also restoring "the original position of the ".?123" key on the iPad keyboard".
Other fixes address "issues where subtitles may not appear in some video apps", and "where Bluetooth could become unavailable".
To get the latest iOS 12.0.1 update, launch your iPhone or iPad's 'Settings' app, select 'General' then 'Software Update'.