Electromagnetic waves do not interact in the space with each other, they are in superposition. But why is that the light at the double split experiment interfers, and we have also dark lines, when electromagnetic waves destruct each other totally. But there are many other examples when electromagnetic waves are not in interaction, only in superposition.
When light produces dark lines on the screen in an interference experiment, the waves don't interact with each other, but are in a superposition, exactly as you described.
Superposition ist just the addition of individual waves. If these waves differ in phase by exactly $\pi$, the result will be zero everywhere, hence darkness. In other places, they will have no phase difference, so they add to create an area with double the brightness. This is nicely visualized in this graph from Wikipedia.
When does interference occur at the light?
Explaining what is happening is not helped by the phenomena being called interference.
In general parlance interference results in altering, modifying or disrupting something.
If you have two beams of light crossing at right angles to one another, there is a superposition of the waves where the two waves overlap but after leaving the region of superposition the two waves emerge totally unaltered from the form they had before entering the region of superposition.
So after emerging the region of superposition a wave is the same as if it had not had another wave crossing it and waves do not interfere with one another in the non-scientific meaning of the word interference.
To get a “visible” pattern as the result of the superposition (interference pattern) certain conditions must be satisfied ie the waves originate from coherent sources.
What one finds is that in the region of superposition the intensity of the light varies with position with there being places where the light is more intense and other places where it is less intense, possibly of zero intensity.
There is no loss of energy as the extra energy passing through regions of higher intensity is compensated for by the reduced energy flow through regions of lower intensity.