First of all, voltage and power are not the same thing. Power is the voltage multiplied by the current. Generating a high voltage isn’t necessarily useful. What you want from a battery is to generate a high amount of power. Then the battery can provide a useful amount of energy to do something.
Another bit of terminology. We tend to call these things “batteries” but they are really “cells”. A “battery” is a group of cells together. What people typically call a C or D battery (aka flashlight battery) is a cell. A 9 volt battery is a battery, because if you open it up, you’ll find that it contains a bunch of cells (typically 6) connected in series.
The voltage of a cell is determined by the materials that are in it. It doesn’t matter if the cell is small enough to fit into a pen-sized flashlight or if the cell is as big as a house. The voltage will be the same. If you want higher voltages, you have to connect the cells in series, as is done with a 9 volt battery or a car battery.
The size of the battery does matter, though. The bigger the cell, the more current you will get out of it. The types of batteries you have been posting about are typically made out of two dissimilar metals with an electrolyte between them. The amount of current you get will depend on the surface area of the metal plates. Plates with more surface area will put out more current, but thicker plates will last longer. So, you have a trade-off when you design your battery. If you want more current, but for a shorter amount of time, you use thin but wide plates so you maximize the surface area. If you want the cell to last longer, you use thicker plates with less surface area. This is the difference between a typical car battery and a “marine” or “deep cycle” battery. A car battery needs to supply a lot of current for a short time (to start the car) so it has thin plates with a lot of surface area. Deep cycle batteries need to last longer, so for the same amount of lead, they have thicker plates with less surface area.
Two other important factors in battery design are energy density and overall weight. Your typical sea water battery has a very low energy density. You’ll need a really huge sea water battery to provide enough current to be useful. There’s a reason people use lithium ion batteries. That particular chemical cell has a very high energy density, and also is very low in weight. A lead-acid battery has a good energy density, but for a given size it does tend to be a bit heavy.
Salt water tends to kill plants if you use it for irrigation. The salt will also contaminate rivers and streams and isn’t good for the environment. This would be an absolutely foolish way to generate electricity on a large enough scale to where this would have a significant effect on the environment. As has already been mentioned, your metal electrodes will be consumed as the battery is discharged. Chemical batteries in general are not a good idea for large scale power generation. If you want to make a sea water battery in your kitchen for fun, just pour the water down the drain when you’re done. Don’t put it in your garden. If you want to generate a significant amount of power, though, find something that is much more practical.