The secondary, output, is on the toroid core.
The primary is lifted above the core, in fact, it isn't even in contact with the core. This is needed to give you isolation at the electrostatic level and series capacitance prom primary to secondary < 1 pf. Call this the ultimate galvanic isolation transformer. When it comes to placing a GND of a probe on a 500v H bridge output, switching up and down in 10ns or less, you cannot bridge that swinging GND to anywhere else in the scope's electronics, or, other input channels. Even a capacitance of 1pf from primary to secondary with a 500v swing at the 10ns rise and fall times would feed a disastrous signal right through a conventional coil sitting on-top of coil transformer. You got to keep those primary and secondary conductors as far away from each other as possible.
Used to do this for audio DAC, not power, but data where you wanted to super isolate the SPDIF signal.
For power, we would use split bobbin transformers to get as far as possible from the mains AC. Obviously, NO Y caps from mains to secondary.
The surrounding black material is plastic. Something very low in capacitance, wont build up static electric charge, and is safe for a few Kv.
That black transformer case goes below the PCB, since you can see a cutout on the PCB. There are 4 solder points on the PCB, not 3. The center 2 on each side is the main transformer connection. It looks like the outer 2 connections on both sides goes to a support wire holding down the entire apparatus. This short outer conductor seems to go through a single loop in the transformer line. Maybe it is a feedback loop. I'm only guessing here.
I believe I once had my similar transformers made at Inductors Inc. I had a 15kv AC hipot. It was a custom job, nothing you can buy off the shelf.