(Not an engineer either) My understanding is that it's been done before on smaller scales but having a giant piston in the tank requires a good seal, railings to keep it straight, and overall way too much mass and rigidity. Consider that the tank walls are only a few millimeters thick.

Instead, it's more common to use gasses injected at the top of the tank to push the liquid to the bottom. Falcon 9 uses helium. Starship uses https://en.wikipedia.org/wiki/Autogenous_pressurization as well as small header tanks for the landing propellants.