The knob hole looks larger than the knob. I want to know if the hole is 2-1/8" (54mm) diameter. If it is, then you have a standard doorknob hole, but the wrong doorknob assembly.
If it is larger than 2-1/8", then have the landlord or home insurer fix it, because this is a big, big mistake! What were they thinking? There is no reason I know of to drill a knob hole oversize. If it is oversize, then decide if you're in love with the door. If not, just replace the door - it will be easier than trying to glue a plug in there, and a lot more secure if it's an outside door.
How to get the knob off
The screws are covered by a vanity plate, because people don't like seeing screws and because they want to be able to change vanity plates for different knob colors. The vanity plate is the pretty cylinder up against the door.
Look for a latch or a catch to release it from the actual backing plate. Also, look for a small tuck-under" maybe 3/16" long, pinch the disc at the points 90 degrees around from there and try to pull it or slide it toward or away.
With a normal knob, you typically need to remove the doorknob, but with that type of handle it may just slide over.
With the vanity plate gone, you should be looking at a steel plate and two screw heads. It's straightforward from there.