The new plumber wants to move the cylinder into attic and make it work on gravity. I take it you agree with him.Could be a thermal store. The pump to the right is I guessed for to rads and just noticed writing on switch confirms that.
So could be stove primaries to the left, (maybe direct connections) and direct flow and return to rads on the right of cylinder.
Mains is perhaps going into an internal transfer coil for hot out. Vessel is misleading as it might be just for the mains pipework, not the cylinder.
If I guessed correct, then seems the plumber messed up with poorly done gravity piping layout for stove and added the other red pump and plugged the stove vent. Unbelievable!
The rep said gravity is no good now for the amount of power stoves is putting out and the pump works better as it agitates the tank.