For example, my phone draws more electricity when the screen is on vs off, and even more still when I’m playing a game, but somehow the battery always provides just the right amount no matter the activity.
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A battery is approximately a contant voltage source. The current it produces depends on the resistance of the circuit attached to it. Current = voltage /resistance. So if the voltage is constant the current will increase if the resistance decrease.
The current is limited by how easy it is for electrons to flow to the circuit. Elections repel each other so one has to move away before one behind it can move and take its place. How easy the electrons can move will that way limit the current.
If you have a tank of water on the roof and multiple hoses that go out from it. The amount of water that flows through each hose depends on the resistance to the water flow of the hose. If you compress the hose you increase the resistance to water flow and less water flows through it.
So the amount of current from the battery works analogously to the amount of water flowing from the tank.
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