The normal approach for drilling half-round holes would be to clamp a scrap piece of material tightly to the work piece, and then drill normally on the join. When the two pieces of wood are separated, you're left with a half-hole in the work piece.
As long as the scrap is clamped tightly and is of similar strength material (e.g. another piece of melamine) this should produce a very clean edge as there is nowhere for the material to tear out to as the drill cuts through it. Of course practice first on some scrap.
To get the flat bottom, you'd need to flat bottomed drill bit, though I'd probably start with centre-drill or regular drill bit to help guide the flat bottom bit into position.
You could alternatively use the same technique, but using a router. With a straight plunge bit or other flat bottom router bit, use that to drill out the hole which may produce a cleaner result and give you better control in positioning the hole.
The chamfered edge can be done with a countersink before separating the two bits of wood.
Fun fact: when IKEA make these in the factory, because the shelves are symmetrical, the "scrap piece" will actually likely be another work piece. That way they can drill out two shelves simultaneously without waste, probably using some giant industrial CNC or manually with a jig.
You can use the same technique if you need to drill out recesses into multiple shelves. Clamp the two shelves back to back (instead of using a scrap piece), and drill as proposed above. This will produce half-round holes in both shelves with half the effort.