We have observed that in some cases the user can not see the blue blinking cursor on text notes. The issue is related with the Accesibility Settings. Please, open "Settings" app then tap the "General" then "Accesibility" then switch off "Increase Contrast" if you want to see the cursor again ;)
Close the Settings app, open Notes Writer then close the document and open it again, you should see the blue cursor.
This is an iOS 13 bug, not related with our app.