Is there a verb to describe an action that can be either "move" and "copy", but in a single word/phrase?
I'm going to stick my neck out and say the answer is No. There is no word which can be used for both move and copy.
Synonyms for move like migrate, relocate, transfer, shift and even ship all involve a real move, where the object appears in a new location and disappears from its origin.
Synonyms for copy like duplicate, reproduce, clone all produce an additional item, leaving the original intact and in place.
There is no word which is ambiguous about whether the original version still exists or not after the operation.
If you're talking about the tasks of copying and/or moving text or code on the computer, they are "commands" usually found in the "Edit" menu of a word processing application - or they can be referred to as "keyboard shortcuts" or just "actions".
Any of those three choices might be suitable for a hypernym for both "move" and "copy".
Presuming a computer theme—such as moving or copying files on disk—you could go with something more generic still such as organize or structure (or restructure). However, these both suggest more than just move and copy and could include delete and sort as well. For the narrower scope, I echo the sentiment of others.
Assuming you're in a computing domain, the C++ standard uses "move" as a hypernym of "move" and "copy". Or actually it uses "move assignment", "copy assignment, "move initialization", "copy initialization", but C++ programmers use "move" and "copy" as both verb and noun to refer to these.
This may sound absurd, but it's quite natural given the technical definitions in the C++ domain. Specifically:
"move" - initializes or assigns a duplicate of the original in a destination location. The state of the original afterwards is not specified.
"copy" - initializes or assigns a duplicate of the original in a destination location. The original is unchanged.
Therefore a copy satisfies the requirements for a move, it is a kind of move. If you attempt to move an object that doesn't have any explicitly defined behaviour for moves, it is copied.
Of course, this only works because of the non-standard use of the word "move" in the domain. In everyday English, "move" does guarantee the final state of the original location, and the object will not be there.
Surely you're just talking about functions which is a hypernym for "any boring shit you can do with computers".
Thus, "< any topic in computing > functions".
or google "file handling functions" "file functions" etc.
(It is Surprising nobody has pointed this out?)
Consider also actions or operations, already suggested.
Can this site ban questions about the use of words relating to computers, or at least require that
the OP states clearly the topic is I'm trying to find a word to use in my "U X" ...?
It's hateful when you get "XY problems" or "goalpost moving" on this site Single word, or good words/phrase for "confusingly asked question where meaning changes."
And it's triply, recursively, hateful when it involves what's the best word! for drop down menu, etc