Can Siri add some form of timestamp to a Note?
No, this is not currently possible using Siri. If on iOS 12 a Shortcut can be made by downloading the Shortcuts app from the App Store.

You can then make this Shortcut:





You can format the date and time as you wish. You can record a phrase for Siri to copy this to the clipboard. After this you’ll need to manually paste it in the note.



Images from https://discussions.apple.com/thread/250089354