The story I was looking for is Quantum Holography by Marcus Holm (June 2016) (also published under the title Quantum Coursework).
It is the fifth result for the following google query: "the duplicate glass" bird
The protagonist starts a simulation on his computer and starts copying things because he does not know how to do better:
Since he still didn’t really understand the format of the data in the hologram,
Anton didn’t really know how to manipulate it. He didn’t know how
to add energy into the system and heat things up, how to push solid objects,
or anything like that. But because he could draw stuff in correct 3d positions,
he knew how to associate spatial coordinates with locations in process
memory. It was enough.
He copies a glass in the simulation:
For the first time, his program produced a sound. Anton heard a distinct
tap when he saw the copy of the glass appear on screen. He zoomed in to it
and observed it closely — it looked just like his used drinking glass, crusty
smear of pancake-greased lips on the rim and everything. He zoomed out to
see how Anton-in-the-screen was taking it.
He erases the copy to cover tracks because the simulation is identical to his reality:
Anton selected a box of air and pasted it over the duplicate glass. It
vanished. He ran his fingers over the spot where the glass stood and felt a
shallow depression where he accidentally cut into the desk. His hands moved
to the Ctrl and Z buttons on the keyboard, but he stopped himself. He
hadn’t implemented an undo function. In fact, he couldn’t implement an
undo function because the old data was gone.
He later copies a bird outside the window:
A bird popped into existence in mid-air, grasping a short twig in its little
feet. It squawked sharply, dropped the twig, and flapped to catch itself before
flying off out of sight.
The story was first posted by author on Reddit in February 2016 and sure enough has received immediate comparison to Off To Be The Wizard. Back then he has stated to be working on expanding the concept to a full novel, but i have no idea whether he went through with it.
