It’s force per area so it’s definitely a pressure, the difference is just that the driving mechanism is chemical potential instead of a difference in number of particles.

Tough a system put into contact with a resevoir of a constant concentration should try to increase in volume until the concentrations on both sides are equal.

It's probably the 'constant concentration' part that is confounding the two. It is connecting number of particles with volume, whereas the canonical ensemble has them as separate terms.