You’re right that electrons, which carry electric current, have mass and are influenced by gravity. However, the gravitational force on an electron is minuscule compared to the electromagnetic forces driving the electrons through a circuit or a conductor.

To give you some perspective:

1. Gravitational Force: The force due to gravity on an electron is given by ( F_g = m \times g ) where ( m ) is the mass of an electron (~9.11 × 10^-31 kg) and ( g ) is the acceleration due to gravity (~9.81 m/s^2). The resulting force is extremely small.

2. Electromagnetic Force: When an electric potential (voltage) is applied across a conductor, it exerts an electromagnetic force on the electrons. This force is many orders of magnitude larger than the gravitational force on the electrons.

Due to the vast difference in magnitude between these forces, the gravitational force on electrons in a circuit is effectively negligible. Electrons “move” because of the electric field (from the applied voltage) pushing/pulling them, not because of gravity.

That said, in the absence of any other forces, electrons would indeed fall due to gravity, just as anything else would. However, in the context of electrical circuits and currents, gravity’s influence on individual electrons is overshadowed by the much stronger electromagnetic forces.

Gravity is the weakest of the fundamental forces. Unbelievably weak. At the scale they are operating on it has zero effect compared to the electromagnetic force. At that scale quantum effects are a much larger influence than gravity. If you, or anyone, figures out how to tie macro gravity and subatomic gravity into one coherent theory then there will be a Nobel Prize waiting.

Interesting question and here is the best ELI5 I could do.
The reason why electrons (charges) don't fall down or bundle up at the bottom is the same reason why dust seems to float. Dust is very light. The force gravity exerts on an object is proportional to its mass. This means that dust particles experience very little downward force from gravity. So little in fact, that small air currents and buoyancy are enough to overcome gravity. Electrons are increadibly light compared to dust, therefore the force they experience due to gravity is miniscule compared to every other force acting on them. This is the case for free floating electrons (ions) as well as bound electrons. Usually electrons don't like being on their own, and whatever caused them to split away from their nucleus had no trouble overcoming the weak force of gravity.
If electrons are bound in an orbiting around a nucleus the forces that keep them in orbit are also way stronger than gravity. While gravity acts on the nucleus as a whole, electrons will not split from them on their own.

To get a little bit more complex, "electricity" isn't a singular thing, its just a broad term for charges and how they behave in electric and magnetic fields. Gravity is also a field. What makes electrons move is the direction of all those fields and their strength. We can't manipulate gravity fields, but by applying voltage that we created using magnetic fields, we can manipulate electric fields. In other words we can tell electrons how to align or where to go. And even very low voltage is enough to overcome gravity.

Because they are different forces.

Gravity has an effect on the mass of an object by distorting space-time.

The particles in Electromagnetism are mass-less but travel through space time. Light is bent from its straight path in large gravity fields but not because gravity effects photons directly but because gravity warps space time.

Think about race car entering a banked turn. The car is the particle and the track is space-time. The car changes direction due to the curvature of the turn.

Can you maybe give an example of when you believe electricity does not getaffected by gravity? I have a hard time undersranding the question.

Because the electrons are bound to the atomic nuclei of the material they are present within. The electrostatic force is much stronger than gravity. This allows materials to exist in the first place, since electrons are the glue between atoms in molecules.

Cables are made of metals since electrons in metals move as if they are part of an electron gas surrounding the nuclei and are therefore free to move around with low resistance.