Hopefully just foam or water condensation over winter. If the bike sat outside and water got in the air box (sounds crazy but it's very possible for rain/snow to do so with underseat filter removed) it has a direct drain into the oil, which would result in this situation.
I don't think I've ever heard of an R3 with a blown factory installed HG.
Doing it in the frame isn't particularly hard. The toughest part IMHO is the bolts that are a challenge to get to because of the frame rail, but it can be done. I think I've done it 4 times now. You absolutely do not need to remove and reseat the cylinder liners as the manual says to do.
It's faster/easier to strip everything away than to try and shortcut by working around things. Harness, coil packs, etc. Free it all and move out of the way or take off if possible.
Head slides out the throttle side(right) of the bike easiest once free, same with valve cover. Once everything's unbolted, a couple of solid rubber mallet taps will get it free(couple up front by radiator, couple back by #3 exhaust port), the factory installed HGs tend to stick a bit.
Don't forget the oil light sensor on the back of the head, it's a bastard to reach but it can be done.