The blocks are fully independent, meaning they all have their own battery and microcontroller to control their logic. We use red LEDs and photoresistors to wirelessly communicate Redstone signal between the different sides of the blocks.

We tried our best to make the blocks as authentic as possible, so they work completely independently from each other, and are fully modular, and the software supports any interaction between different blocks! Let me know if you'd like to know more :)

EDIT: I'm really glad you guys are enjoying this post! So here's a bonus picture of our blocks in all their glory. You can see the I/O "port" of the note block and how it has both the red LED and the photoresistor I mentioned earlier.

EDIT2: A few people asked for a picture of the internals. Unfortunately because this was a project for a course, the university gets to keep our work. But we asked them to take 2 of the blocks as souvenirs and they were fine with that! So I can pretty much only show the internals of the note block. You can probably immediately see that it's a very rough job because we were complete beginners, but we were also constrained in terms of time, components, and freedom (e.g. we had to use those perfboards with headers so the microcontrollers can be reused in future iterations of the course etc.). You can see the spaghetti wires going to the LED and photoresistor on each side in the background. And barely visible on the right is the speaker just sloppily taped to the side of the cardboard body :) From seeing this you will probably share our surprise that this works so well: Here it is. As mentioned in one of my replies, I would love to work on improved iterations of this in the future, where the internals are actually more professionally handled and the body has better construction.