What arc threshold voltage and current do you want?
Making the electrode is not hard but defining/controlling the gap area for its electrical properties is the key. So I guess you start by copying existing ones. Also the capacitance of dielectric like water is 80x air.
Here's a DIY version on YT.
My transformer will give after rectifying and a large cap have an open circuit voltage of ~98VDC, and then a bulk resistor will take the ~20A down to 15A. The transformer is a used one from a servo drive and I can't find any specs on it, the company went out of business. So then the cutting/burning voltage is the in the 50VDC -20VDC range after the ~98VDC ionizes the oils dielectric. Those are the parameters most all industrial machines use.
When you say water as a dielectric your talking about wire EDM. Sinkers use oil. When the company bought 3 new Charmilles CNC sinkers the front office said we had to use deionized water like the wire machines. But a wire has very little debris from the cut, where the sinker has much debris, When the company that supplied the deionizer tanks started charging big bucks to clean and replace the deionizing medium they soon let us go back to using oil.
The circuit you got from Youtube is similar to the ones most all of the youtubers are using. Basically just switching a high amperage DC on and off with a PWM circuit. If you look at those guy's machines when they are burning you see very large sparks, but then if you look at Reliable and another good Youtube channel, "learn to burn" their sparks are much smaller and more controlled.
Another reason for most of Youtube's doing what they are doing spark wise is because of their ram drive/motors. most are using a small DC gearmotor and a fine thread lead screw. So in essence they have little to know control of the gap. So they make the spark generator more powerful instead of controlling the ram advance better. You can get more control with a stepper motor and a coarse thread, and use micro stepping control. With that setup you can make each move of the motor 0.001 which is the preferred gap distance. Then you work on getting the sparks more under control.
If you read in the PDF you posted on page 140 last sentence in the first paragraph, they say it all when it comes to sinker EDM, paraphrasing, "controlled sparks" is the key. Using the circuit you posted there is no real control of the spark, it's either off or on at full voltage.
EDM is slow work, so while the machine was burning the job I was reading all of the manuals for the machines we had. And trying to understand the process better, I bought a couple of text books on EDM by people who taught it in college, then started to try to learn electronics. I know what a machine should do but am having a hard time putting it into getting the electronics to work.