I think head gasket (never seen this color and I would never start with that so good you took it out, maybe heat some on a spoon and see if water is present?)
But starting in winter without driving means it does not reach operating temp and so no water was removed from the oil by idling.
The Hot Pan Test is one of the simple tests to measure water in oil
Maybe put some of that oil in a jar and see how it separates at room temperature (oil floats on water after a while) and maybe use a bit of new oil with coolant to see if you can replicate?
But condensation in the cold is a lot when looking at months of time. When around 0 degrees celcius more condensation was visible on my fuel-tank and engine.
I keep the fuel tank full to prevent condensation inside.
And when replacing the air-filter my GSXR1000
had to much water in the crankcase breather filter, maybe check the air-filter box?, it has a drain that was dry.
I don't think it can drain back from filter to engine, but maybe...
air-filter cover inside, squeezed filter in paper:
Top cover of the air-filter, breather GSXR1000 2014
The GSXR1000 2014 airfilter water drain was dry, so that is not really an indication to me:
Add water to oil, still kept going:
The Gixxer forum messes up the attachment pictures, on the original website they can be clicked and zoomed: Suzuki GSX-R 1000 2014 = L4 WVCY/12