I am wondering if it is possible to install a built in cistern next to the toilet. Please see the image attached - the idea is to have a cistern in the short dividing wall next to the toilet bowl. Cistern would be installed in the right angle to the toilet. I am not worried about the gravity drop, as the wall could be slightly taller than what is on the image attached.
If you step back from "cistern" you've no doubt encountered "tankess" pressure-flush toilet at most public restrooms, either with a pipe like this, or with a button on the wall and less visible/exposed piping:
In a typical house, you'll need a very local pressure tank and some large supply pipe between to support these things, which are designed for buildings with a much more robust water supply.