What size wire for a 60 AMP panel 400 feet away?
Do we care about money here?
An oddity of wire economics is that 2-2-2-4 &quot;MH Feeder&quot; (90A; 100A if service) is about the same cost as 10-3 UF-B cable (30A).  The difference is aluminum, which is absolutely fine for large feeders of #2 size.  (not so good for #10, but not our problem).
Big big problem: your loads are 120V
Given your application, the power usage is 120V and wildly lop-sided onto one leg.  This means you really need to do your voltage drop calculations on 120V not 240V.   Which really throws a wrench into it, unfortunately.
The 120V load is probably at least 10A (since it's demanding a 20A dedicated circuit) but should not be more than 16A continuous as that's too much for a 20A circuit.
And when we consider voltage drop at 120V, that's a very grim picture.  The minimum legal size is #10 copper, but that's right out, giving 11% voltage drop at 16A.  We have to go clear up to #6 just to get 4.71% drop, but that makes more sense since it's much more expensive than the MH feeder I mentioned earlier.
If we go with the 2-2-2-4 MH feeder, we're at 3.13% which is completely acceptable anywhere but maybe Canada, and even there it's within the margin of error, for Pete's sake.
The aluminum feeder will work fine since we are going panel-to-panel, so we're running between lugs that are either made for aluminum, or are aluminum.