Everything is controlled by a PIC micro. But almost any microcontroller will work as long as it has enough input/output pins to handle whatever you need to do. I designed 2 boards I commonly use. One uses an 8 pin pic chip (5 I/O). That use 2 pins for inputs, 2 for outputs (leds etc) and 1 for controlling the wt588 module in single wire mode. That's for really space constrained builds.
The other board I use an 18 pin PIC which has minimum of 13 I/O. For that one I have 4 inputs, 4 outputs (leds etc), 1 for the sfx control, and then a couple for and I2C or spi like interfaces. There are 4 digit digital displays that are driven by 2 lines which are handy for things like pulse rifles
Even that board fits in the grip of the PPG though so its not huge.
One of my outputs is always connected to a logic level mosfet. Which is capable of driving several amps. So with the right resistors and using a short pulse you can actually drive 1 or more leds at a current that would normally destroy them if you just turned them on. But because its on for a very brief period it doesnt burn up and you get a very bright flash. The same mosfet can also be used to drive a motor if needed or any other moderately high current device.
Code was all done the hard way, no libraries like you get on an arduino, but that's cause I have my own. Also with my stuff having to transmit very precisely timed IR pulses the arduino timers aren't precise enough to work reliably so I just rolled my own. You are probably better off using a micro that does support the arduino libraries as that's not going to be a factor for you. Will make coding much simpler.
The thing about most microcontroller families is that nowadays they are all pretty similar, they come is all sorts of packages and the requirements to run them are all very similar. So you just pick one that has the the peripherals you need (if any) and that you can get the programming setup for.
Your biggest problem from what I can tell is that you will have to learn to read and interpret electronics data sheets (which are not designed to be straightforward), then work out a schematic with all the 101 electronics design rules and gothchas for the myriad of components available, translate that schematic into a board layout using some pcb design software (such as KiCad) and then get them made and hope you didn't miss anything. Then you have to program up the boards using a suitable programmer as you cant just plug in a USB cable. It is a VERY steep learning curve.
Its not impossible, just difficult. And possibly expensive.
Its why most people use a ready made board and environment like the arduino's where you can just plug and play and get right to the coding stage.
As for the OEP3W, well I have about 9-10 left but I also use the XPT8871. Its a bit louder than the OEP3W and uses a bit more current as well as being a bit bigger physically.
Modules from the chinese sites come and go for availability which is where knowing how to test and figure out any interfacing components required is handy. With them being cheap I generally buy samples of anything that looks interesting. I've just got in 2 more types of amps that I need to have a play around with and see if they are any use. At least one of them should be a good replacement for the OEP3W.
Feel free to drop me a PM and I'll shoot you my contact details if you want to discuss anything in detail. I think you are in the UK too aren't you ?