Uh, what a pitty
My garage says it can be differential and that wouldn't be a cheap fix...
I think I can start with urethane motor and transmission mounts
I even put a gropro to underbody to shoot the transmission movement cause didn't see such a video anywhere, hoping to upload to youtube soon.
Anyway, there is movement but nothing exceptional.
On the other hand, 2010 with 47.5k miles on clock, it shouldn't be worn out diff, engine and transmission mounts might be aged already, garage checked transmission mount and said is not bad, still holds transmission, they had much worse cases on 370z.