The fact that her suspicion weakened when they actually tried is the best imo
It's the opposite actually.
This whisper war is basically both of them being petty and try to bait the other into making a mistake by using the threat of Rosee.
It's like 2 school kids making funny face at each other hoping to make the other laugh and get yelled at by the teacher.
So their focus went off from Rose to each other, which make Rose confused because this is not a professional behavior she expected (also Rose thought they're from the same faction which make the 'infighting' even more confusing)
On the potential ship of these two:
Hibai's too laidback and doesn't mind the status quo, so Gina's gonna be the one pushing/pulling the relation along.
Then Hibai top her in bed anyway.