Apparently I'm pretty far off, but just this idea of animals communicating images with sound waves was something I'd otherwise never have.
Some people see colors or feel tastes... and it doesn't seem that unlikely that there would be selection pressure for parts of the bird brain to connect their spatial awareness to their auditory system and then songs. There could be a nice feedback loop that their own songs would strike similar experiences for themselves (if they hear themselves similar to others).
Of course we know that bats have this type of neural connection in echolocation and dolphins/whales may even using it to communicate in similar ways with their songs.
If you place migratory birds in a big round cage, they show 'Zugunruhe[0]', or migratory restlessness: they jump and flutter in the direction that they would be otherwise be migrating if they were out in the wild. Rotating the magnetic field (e.g., by putting magnets around the aviary) also rotates the direction of their Zugunruhe.
No one totally understands how this works, but the magnetic information is thought to be 'overlaid' on other sensory information. One candidate pathway involves a light-dependent pathway in the retina. When a cryptochrome absorbs light, it generates radical pairs that affect how visual information is perceived[1]. This could give the birds something like HUD which displays magnetic field lines on top of the visual scene. Consistent with this idea, birds can only orient to magnetic fields under certain colors of light, with the color varying a bit from bird to bird[2]. It's almost as if the colored light washes out the HUD.
There's another parallel pathway involving bits of magnetite in the beak[3,4]. These signals flow through the trigeminal nerve, which carries a lot of different signals; it would not be impossible for this to manifest as "pressure", as it carries touch/somatosensory information in many animals.
[0] Ethologists love German and this word captures my lockdown feeling so very well. [1] https://www.sciencedirect.com/science/article/pii/S000634950... [2] https://www.nature.com/articles/364525a0 [3] https://www.sciencedirect.com/science/article/pii/S000634950... [4] https://royalsocietypublishing.org/doi/10.1098/rspb.2009.005...
Perhaps it's good to know that the x axis (from left to right) is temporal. So for someone/something to translate this to an image with some special sense would also necessitate some memory part.
With a big fantasy you could continue your hypothesis by comparing it to describing an object you see with words by telling the height of the outline from left to right.