This isn't a full answer, but I hope the advice helps:
- Expecting readers to reverse-engineer the circuit from a photo is IMHO too much. More research (including producing a schematic diagram of the wiring) is needed first.
- Read the part numbers off the four (3-pin?) devices attached to the rear metal plate, find their datasheets and hence their pinout, to help you produce the schematic.
- I doubt that using only the 2 red & 2 blue wire pairs you mentioned, will be sufficient. Notice that some black wires also go to those four devices (although the full wiring is too cluttered in the photo to be clear to me).
- Also notice that the various "control wires" (red, blue, black etc.) are too thin for carrying 30A. Therefore I disagree that the four devices are diodes forming a rectifier as claimed. Instead more likely to be triacs, perhaps?
- You say that the previous PCB controller has failed. However that PCB will likely contain clues, to help you recreating its functionality (which seems to be your plan).
When you have produced a correct schematic, you will have a better chance of designing how to interface it to an Arduino as you mentioned.
Interfacing with mains devices also has inherent safety concerns, which is another reason you need to start with the correct information e.g. to minimise the risk of something exploding and causing injury to those nearby, or causing electrocution, or causing a fire etc. etc. If in doubt, consider whether the risks of DIY are worth it, and whether your skills are at a level where you really want to attempt this project. There is no shame in deciding that the risks are too high. Good luck whatever you decide!