I’m also still using the 6S+ and finally updated to iOS 12.1.4 from iOS 11 about a week ago, and today (2-25-‘19) had the same experience as others in this “thread” when attempting to include info in the “Notes” section as i was adding a new contact: hitting the “+” at the top right in “Contacts”, to add a new “contact” takes me to the same entry fields as hitting “Edit” at the top right in an already existing “contact”. Those entry fields allowed as before (pre-iOS 12) all the data to be entered to create a new “contact” or to edit an existing “contact” EXCEPT that the entry field for “Notes”, which WAS allowing editing in that field (while in “Edit”); but ONLY if the field already had had data entered. That is — IF the field was blank (as with an existing contact that hadn’t yet had any “Notes” included), OR (while in “+”), when creating a new “contact”, (since no data had yet been entered in ANY field) — in which cases the “Notes” field was not accommodating the entry of any “notes” at all. Again: all the “Edit” and “+” entry fields in “Contacts” worked as before iOS 12 (for me) EXCEPT “Notes”, no matter how many times i tapped on or below “Notes” as some suggested; or how many times i re-booted the device as others suggested. Finally, after reading what “Mneugarten” wrote in response to “arfedden” regarding mistakenly assuming a need to press “Edit” to edit “Notes” - i experimented with seeing whether it was possible to enter data in the “Notes” field without hitting “Edit” at all, by simply hitting “Notes” in an existing ‘noteless’ “contact”; or in a newly-created but as yet ‘noteless’ “contact” after hitting “Done”. I discovered that it is possible to enter or add to “Notes” without hitting “+” or “Edit” at all. As to whether or not that is a good thing, (in that it may make accidental deletion of “notes” more likely), i haven’t yet reached a decisive opinion.
After having entered some new “notes” without having gone into either of the “Edit” or “+” (add new “Contact”) modes, i found that now that i have done so, i am also able to enter new “notes” while in both those modes (“Edit” and “+”). In other words: I have no idea why; but somehow it is now fixed. I hope this helps someone.