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Total drag / friction drag at your speed. Waves lose energy as exp(-2gh/v²) with depth, so a swimmer a few body diameters down escapes the penalty.
The science
Drag. A swimming otter pushes water aside with its skin and body. Friction drag is Df = ½ ρ v² S Cf FF k with the turbulent flat-plate coefficient Cf = 0.455 / (log10 Re)2.58, Re = vL/ν, the Hoerner form factor FF = 1 + 1.5 (d/L)1.5 + 7 (d/L)3 and a stroke-augmentation factor k = 1.4 (a moving, undulating body drags more than a rigid one).
Wave drag. A body moving at the surface makes waves, and the waves carry energy away. The wave length of the main transverse wave is λ = 2π v² / g; when it equals the body length the Froude number is Fr = v / sqrt(g L) = 0.399 (hull speed v = sqrt(g L / 2π)) and the penalty is steep. A submerged body feels the same wave field weakened by exp(-2 g h / v²) because the wave motion decays with depth like exp(-k h) with k = g/v². Here the extra drag is Dw = Wmax Drigid exp(-(ln(Fr/0.45)/0.6)²) exp(-2gh/v²) with Wmax = 4. That bell shape is an illustrative fit to the trend reported by Hertel (1966) and measured on swimming mammals (Williams 1989): a surface swimmer can pay up to a few times the deep-water drag around Fr 0.4 to 0.5.
Energy. Mechanical power is P = D v; muscle and propulsion turn chemical power into it with an overall efficiency of about η = 0.15 (typical, illustrative). Resting metabolism is taken as 2.4 times Kleiber's 3.4 m0.75 W. In cold water the heat loss G (Tb - Tw) may exceed exercise cost; heat from swimming substitutes for it, so the model uses the larger of the two. Fur traps air; by Boyle's law the layer shrinks as 1/(1 + h/10.33 m), so conductance grows slightly with depth. Cost of transport is COT = Pmet / (m v).
Aerobic dive limit. Oxygen stores of about 40 mL per kg (typical value, not measured on one animal) are used at Pmet / 20.1 J per mL. When they are gone the otter must surface; with Dive cycles on it returns to the surface and refills.
Honest simplifications. One body length and wetted area from geometric scaling of an 8 kg otter; no real stroke-by-stroke thrust, no turbulence, no free-surface breaking; the wake is drawn from linear (Kelvin) theory with only the transverse waves, amplitude exaggerated by four; the constants above are plausible, not fitted to a particular otter. Use the model for the shape of the trade-off, not for exact watts.