That's a thermal rectifier circuit. it's making 281V DC from the AC coming out of the transformer. Something then happens further into the circuit and you end up with a slightly lower DC voltage, that's the 268VDC .

AC voltages are always measured as RMS value. Their peak value is sqrt(2) x higher than the nominal RMS voltage so 281/sqrt(2)=198VAC --> ~200 VAC which is an oddball voltage but whatever. So you have a couple options:

-buy a 120V:240V and remove a few turns of wire from the secondary side so it makes 200VAC instead (https://www.amazon.com/Simran-THG-1000T-Voltage-Transformer-Converter/dp/B01HUDSDVW)

-buy a 120V:240V and make it fight one or more small low voltage transformers (EG:240-16-24=200V)(no messing around needed but it's a bit ugly.)

That transformer or transformers would produce 200VAC or 282Vpeak. You can connect that to a full bridge diode rectifier to produce an approximately 281VDC supply.

That's if you're willing to get rid of the thermionic rectifier tube. If you actually want a transformer like that shown in the schematic, center tapped then yeah, you'll have to wind it yourself.