The mention of "Servo motor" essentially means a variable motor controlled auto-transformer. See
https://variac.com/staco/PDFCutSheets/VT Schematic.pdf (No motor). They are usually single winding with a brush, non-isolated. It's important to fuse the wiper. They can be configured as buck-boost.
Transformers and motors are rated in VA or Volts*Amps. For resistive loads, this is equlivlent to Watts, but for inductve loads (motors) it isn't. Initially, the service needs to be able to supply a brief burst of current equal to the resistance of the motor winding, A little rule, like the "current in an inductor can't change instantaneously" comes into play.
The US doesn't put fuses in the cords like the UK does.
What's the VA rating of your USA appliances and what is the maximum current a typical UK outlet can deliver?
Would you have all of the USA devices operating at the same time?
Now, you sort of, see the need for two 20A 120V services in a kitchen. Microwave ovens might be separate because they are close to 1500 VA. Electric stoves are usually 240V and would have a separate service. Some stove tops and ovens even if gas might require a bit of 120 VAC.
The NEC would like you to have what's called 4-wire 240 for your electric oven and electric dryer, This has L1, L2, N and Ground. it's (L1)120V-(0VAC)(N)(G)-120V(L2) which is just a center tapped 240V transformer.
For a 0-120V secondary, your secondary (N) would get bonded to ground as a separate wire.