I thought I would include this video in case any other pet owners are suffering an unexplained massive increase in their water bill.
These owners certainly have a smart cat!
I suggest the best way to fix the problem would be to close the bathroom door (and possibly make the sure the latch on the outside cannot be easily opened) and to make sure the lavatory seat is never left open. Possibly covering the flush mechanism with something that could be easily removed by humans only would be another solution.
Fortunately we have a toilet cistern with a dual flush system, and the buttons are on the top. Our cat Gilbert is largely Maine Coon, and is so large that if he tried to stand on the toilet seat to press the buttons he would probably fall in! Luckily he has never shown any interest in the water inside the bowl or the flushing mechanism. He does know how to push latches down and open doors however (something he must have learnt at his previous owner’s house), but luckily we have round door knobs and they are beyond him. If the door is ajar he stands on his hind legs and pushes it open before strolling in, and he always stands up outside closed doors and tries to poke the handle with his paw.