Steam turbines work not because of steam alone, you can fill a room with steam insert a turbine and nothing happens. To get them to spin you need higher pressure on the input side of the turbine than the output. If you want to have steam go up a shaft that’s going to increase the pressure on output side and thus reduce the amount of energy generated by the turbine.
Yes, it's the difference in pressure/heat that is exploited, as Sadi Carnot noted (by analogising the steam engine to a water-wheel exploiting a fall of water, treating it as a "fall of heat")
Steam turbines work not because of steam alone, you can fill a room with steam insert a turbine and nothing happens. To get them to spin you need higher pressure on the input side of the turbine than the output. If you want to have steam go up a shaft that’s going to increase the pressure on output side and thus reduce the amount of energy generated by the turbine.