You can use the 10/2 all by itself.
There is a common misconception that "everything needs neutral" in US circuits. But that is not actually the case. Only devices that need 120V need neutral, including devices that need both 120V and 240V (e.g., clothes dryers). Devices that only need 240V (water heaters, air conditioning compressors, etc.) do not need neutral. Based on your wiring diagram, your steam generator does not need neutral. So two wires are all you need.
There is another common misconception that "white = neutral". That is not true. Neutral is always white (or gray). But white can also be:
- Second hot in a 2-wire cable (your situation)
- Hot in a switch loop cable (prior to "neutral required at all switches" rule)
It is possible in a retrofit situation to add a separate ground wire (green or bare) outside of a cable. But ground is not neutral, and this is a new installation, and you already have a ground wire.
As far as why you can't (if you needed neutral) combine a 10/2 with a single wire: There are a bunch of reasons, including the issue of how the hot(s) and neutral wires interact (keeping all the wires for a circuit together has some real benefits), individual wires are not protected the way cables (whether NM or armored cable) are protected from damage, and the very real possibility that if you have an individual wire outside the main cable that it could get damaged - or simply removed by someone in the future who doesn't know why it is there.
As far as wire and breaker size: 10 AWG is good for 30A. If your steam machine actually uses a full 25A and is classified as a continuous load then it would need 25 * 1.25 = 31.25 A, which push it up to a larger than 30A breaker and wire size.
If it actually only uses 24A (or less) continuous then 10 AWG wire and 30A breaker is correct.
And if it actually uses 20A (or less) continuous then you still need 10 AWG (unless 16A or less) but a 25A breaker is fine. (I actually found out about that recently - my air conditioning compressor was on a 30A fuse and 10 AWG wire, but my electrician put it on a 25A breaker based on a nameplate rating of 16.1A.)
So the meaning of "needs 25A" will determine the wire and the breaker.