How to remove this door knob and plate with no obvious screws
There's a tool provided with the lockset that engages the heavy ring just inside the finished escutcheon. You can see the two opposing slots on the outer edge. The tool looks like a skinny metal shot glass with two tabs protruding straight out from the cup lip. You'd fit it over the shaft, engage the slots, and turn.

You can try poking the points of a needle-nose plier in there and spinning it out counter-clockwise.