I was having the same issue. When searching for a contact by name then opening the contact, and pressing edit, the option to delete was mysteriously absent.
I found a solution. Instead of using the search feature to find the contact, I scrolled down and found the contact alphabetically. Then when clicking the contact, then edit, the option to delete contact was back where expected at the bottom of the screen in red.
It seems like a bug that it is not there when searching for the contact. These days we are all overloaded with contacts to the point that most everyone searches instead of scrolling through long contact lists. I hope this gets fixed.
For now, I hope the workaround helps.