Understand why your camera's serial number may not be displayed in the Preferences dialog box.
The serial number of your camera model isn't displayed after you select Show serial numbers in Camera Raw Preferences.
Some of the older camera models such as Sony A9 or Sony A7iii did not include the camera's serial number in the metadata of their raw files. Hence, you may not be able to see the serial number in Preferences.
The newer camera models such as the Sony A7R Mark IV, support the writing of the serial number in the raw file's metadata. In this case, you will be able to see the serial number listed in Camera Raw Preferences.