I recovered from some PCBs some displays of this type, I also have a common cathode display and a common anode, I also bought some 74hc595. I want to make the PCBs, but first I want to ask your opinion, if the circuits are made correctly, because they are not so easy to make at home.
That module on the internet does not have resistors, so it relies on the 74HC595 to limit the current and it does not have decoupling capacitors.
We prefer that you show the pictures here.
I think the schematics are okay. A single 100nF for both 74HC595 and a single 10µ (or more, 47µF ... 470µF) for the led display is probably enough. One or two more 100nF does not hurt.
The schematic can be made prettier if you move the top 74HC595 to the lower part.
You have to fix three NPN transistors (Emitter <-> Collector).
MAX7219 is for up to 8 digits but can be programmed for less (from 1 to 8), is cheap and the scheme is relatively simple. If you use 74HC595 more elements are needed and the program will be more complicated because you have to take care of the appropriate fast multiplexing of the digits. MAX7219 takes care of multiplexing and has overall brightness control. The choice is yours.
Okay, so you have some parts and you want to use them even if it's a harder way, a lot harder. At least do you have ULN2803? It can replace your pile of transistors and resistors.