The stopper. It is leaking out of the part where the nut attaches the pivot rod to the pipe. I assume this is because the pivot rod is not properly inserted into the stopper, and as such the nut is not able to screw on properly.
That’s some seriously bad design. Taking out the stopper for cleaning is normal maintenance and shouldn’t require specific skill to put back. Still, you reported it to your landlord, everything that resulted from it further is on the landlord. If you really broke it (doubtful) the landlord should have fixed it and maybe send you a bill (debatable). Leaving it broken is what caused this mess.
The stopper. It is leaking out of the part where the nut attaches the pivot rod to the pipe. I assume this is because the pivot rod is not properly inserted into the stopper, and as such the nut is not able to screw on properly.

That’s some seriously bad design. Taking out the stopper for cleaning is normal maintenance and shouldn’t require specific skill to put back. Still, you reported it to your landlord, everything that resulted from it further is on the landlord. If you really broke it (doubtful) the landlord should have fixed it and maybe send you a bill (debatable). Leaving it broken is what caused this mess.