I would classity it as a noncontinuous load and use a 25 Amp OCPD per 210.20 (A).
This would allow the use of #10 Cord rated at 25 Amps as you supposed from 400.5 (A).
My reasoning would be that the load consists of 3 parts. The water heating element, surface warmer and 120v indicating lights and or timers etc.
The water heating element which draws the most current for this type of appliance will only draw for the short time when the appliance is first started, leaving a much lower current draw while warming only.
HTH