Three possibilities come to mind here
In wall tank gravity flush system. Tank is actually in the wall and uses gravity to flush the bowl. Requires reframing the wall to accommodate the frame, moving the drain to come up the wall, and potentially moving vents in the wall and anything else thats there. As quiet as any gravity flush tank style toilet
A stand alone smart toilet/bidet/heated seat. Flushes using water pressure. Mounts on your normal 12" rough in. Requires 120v power to operate. Washes your behind. Heated seat.
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