Last thought. With the top off press ,in turn, each of the white and blue levers ( one at a time. )
I presume it must be a dual flush, ie, two buttons, one short flush, the other a longer flush.
Push down and quickly release finger to allow flap to spring to original position and see if outlet is effectively sealed.
These things work by lifting a plug out of the hole in the bottom of the cistern releasing the water. Usually the weight of water in the cistern is sufficient to keep the plug with it's rubber seal watertight.
Keep us posted.