Energy isn't really a thing. It is more like an accounting system. So asking what it can do might not be the best question to get at what you want to know.
You have an isolated system. Energy is some numbers you calculate or measure based on where pieces of the system are and how they interact with each other. The system undergoes changes. Pieces fly around, bounce off each other, and such. You repeat the calculation and get the same number. This is the nature of conservation of energy.
It is not like an isolated system that has a certain amount of water in it, where you find the same amount of water before and after.
To see this, consider a rock floating in space. Two spaceships pass by at different speeds. Each sees the rock moving at a different speed, and calculates a different kinetic energy for the rock. Both are right, as is the ant sitting on the rock. The amount of energy is dependent on the frame of reference.
It is common the think of energy as a kind of stuff that lives in the rock and can be transformed into other kinds of energy. People use this approach because it gives right answers as long as you stay in the same frame of reference. I often do it myself. But this doesn't describe the real nature of energy any more than velocity is some kind of stuff that lives in the rock.
When dealing with general relativity and curved space-time, it can be impossible to find a frame of reference that covers everything. It is hard to come up with a definition of the total energy of the universe. You can do it for fairly large pieces of the universe.
So the question you want to ask is what kinds of things do you have to add up to get the same number before and after. This tells you what kinds of energy there is.
For more on conservation of energy, see https://www.feynmanlectures.caltech.edu/I_04.html
You already know about kinetic energy. $E = 1/2 \space mv^2$ unless speeds are relativistic.
Suppose two charged particles approach each other. Their repulsion slows them to a stop. This is because of a force that acts as the particles travel a distance. It is the work you mentioned. You now have no kinetic energy, but when you calculate potential energy, you find the same amount. And it shows why it is useful to think of transforming energy from one form to another. Classically, $E = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r}$
When charges move, there are also magnetic forces.
An atom has an electron in an excited state. It decays to the ground state and simultaneously recoils. A while later, another atom experiences a recoil in the opposite direction and one of its electrons is promoted to an excited state. A photon is what happens in between. To make energy balance, you need to calculate kinetic energy, the energy of an electron in an excited state, and the energy of a photon.
Notice that a photon is created and then disappears. Quantum mechanics doesn't say how an electron creates a photon as it drops to a lower energy orbital. It just gives the states before and after. This is part of the reason that asking what energy does may not be the right question.
The energy of electrons in various orbitals is calculated with quantum mechanics. The idea is the same as classical forces between charged particles. But when a particle is as small as an electron, the uncertainty principle prevents you from knowing where the electron is. The calculation is difficult in all but the simplest case (H atom). It is easier to measure, and perhaps easier still to look up.
Calculating the energy of a photon is also done with quantum mechanics. The result is pretty simple: $E = hc/\lambda$ where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength. It is also easy to measure.
Two atoms approach each other. They collide and form a molecule. You find less kinetic energy. This leads you to look for a way to calculate energy of bonds. You can sometimes use a classical approach, where positively and negatively charged atoms attract each other. This is good for ionic bonds like Na+ and Cl-. Covalent bonds are formed when nuclei get so close that electrons enter orbitals that go around both nuclei.
Objects contain many atoms, and these atoms are never sitting still. This is often called heat, but the more correct term is internal energy. Heat is really used for transfers of energy involving temperature changes. Internal energy is the total kinetic of all the atoms plus the potential energy from all the bonds.
There is potential energy from gravity. This is very much the same as potential energy from electromagnetic forces. But of course gravity is a completely different thing than electromagnetism.
There are two more forces, the strong and weak nuclear forces. These bind particles in a nucleus. They act only over extremely short distances, and can only be described quantum mechanically. There is potential energy associated with these forces.
Light is photons. It is sometimes convenient to add up the energy in each photon. But sometimes a classical approach is better. For example, microwaves are low frequency light, typically containing a great many photons. They are generated by the motion of a great many electrons. It is easier to measure the total electric and magnetic fields from all these electrons than to keep track of the photons generated by each electron. Light is also described by oscillating electromagnetic fields. The energy can be calculated from the amplitude of the fields.
Oscillating masses can generate gravitational waves. These waves carry energy. Normally this is tiny. But under the right conditions, it can be huge. This was recently measured by LIGO. The first detected wave was from the collision of two black holes. In the final 0.1 sec, two stars much larger than the sun were orbiting each other 40 times a second. The final black hole weight 3 solar masses less than the original pair.
This brings up $E = mc^2$. Mass is associated with energy. Mass can sometimes vanish or be created. Energy is still conserved in these cases. The energy in the gravitational waves was given by this equation, where $m = 3m_{solar}$. In that 0.1 sec, the collision radiated more energy than the rest of the observable universe combined.
Another place for this is when an electron and a positron collide. Typically they vanish and are replaced by two gamma ray photons. Photons have no mass. The energy of each photon is $E = m_ec^2$.
As new physics discoveries are made, the list of things to add gets bigger. Often the ideas behind them get more complex and strange.
Astronomers looking at galaxies noticed that stars rotated around the center faster than could be explained by the gravitation attraction of everything visible. They considered what might be there without being visible, and ruled out various possibilities. In fact, they ruled out everything. To explain it, they proposed some unknown form of "dark matter" that doesn't interact with light.
Empty space can contain energy. Observations of the expansion of space showed that the expansion is not slowing down as expected. It is accelerating. The amount of space is increasing in an unexpected way. The current understanding (to use the word loosely) is that this may be caused by some unknown form of "dark energy".
See this for more: https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy