Is Otani a Pitcher or a D.H. Who Pitches?

The MLBPA logo shows only a batter and feeling that it reflects an underlying bias, pitchers decided to form their own union. Would Otani join the rebels? And more generally, what would be the effect of separate pitcher and batter unions each negotiating separately with MLB? The whole point is that he's all those things. Like, why would we classify him as one or the other when the whole wondrous unicorn nature of Otani is that he is allThings.