I feel with Alvin stating a 3C was a priority and the close relationship with Milstein, I think Vancouver goes hard after him. From Barbishev's pov, he gets to play with several fellow countymen which given the times might be a draw, especially if he's got a family.
He also likely gets a boost playing behind two C's that are capable of 90+ points.
From a nucks pov, they are the 5th youngest team that needs to add more solid vets to fill out the core since as of next summer the only two players signed over 30 are OEL and JT. The fact that he plays all 3 forward spots is a plus since he can move around if/when one of Raty, or Linus Karlsson can stick at C.
Contract wise you gotta figure with the cap going up and shitty UFA centre crop, 5+ over 6 years?
If so from a nucks POV our Centre depth goes from EP, JT, Horvat, to EP, JT, Barbishev, while saving money and term over Horvat, while adding, Beauvillier, Hronek and Raty, minus whatever it costs to move Myers to create cap space.