Nice work. I like these types of projects. What is exactly the chip that is processing the code? I mean, the ESP is only for internet connection, right (I have my own but never used it, :p) ? So, what is the chip you're using for the process of communicating with the LED matrix?
The ESP32 is a very capable little chip; it handles WiFi and all the logic for controlling the LEDs. No other chips involved. The setup looks exactly like in the picture above with the shield stuck directly to the back of the matrix and the ESP32 on top of it.
Regarding its capabilities:
Someone emulated an IBM PC with FreeDOS on it, running on one of these... 
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Here's a video where you see the hardware as well.I am actually trying a small project myself, but I lose the drive frequently and I end up giving up now to come back to it some time later. I'm using an stm32L412 chip to control a fan that is supposed to cool my NVM2 drive of my LN node, using a thermistor and a couple other additional components, however, this stm32 is proving to be a little bit complex to learn and get along with it!
Well, if you're within the Arduino 'ecosystem', while not being best for performance and all that, it's pretty easy to quickly whip up something that works, especially due to all the libraries that are around. This really didn't take me more than a few hours. In fact, I rushed it to have it up for the 19M BTC milestone and only had a few hours left when I got that idea. Later I put in a little more time to clean up the code and make it more readable for this post.
Oh ok. I never dig into ESP32 too much.
Anyways, about STM32 is an whole new world. Arduino and such platforms are all based in 8bit chips. STM32 it's, well, 32bit. So, there's a lot more to setup before you can put it to work. Schematics and block diagrams are an whole new level. At least for me. I did my graduation project with a bare AtMega328 and some additional electronics and yes, that one was kinda easy to grasp! Well, at least if you want to use non-proprietary libraries. HAL libraries for STM32 are a bit confusing and I gave up on them and started using libopencm3.
Ok, hope you keep improving on your design and features of your project. I'll keep taking a look to this thread!
Thanks for sharing!