The Barzan are now part of the Galactic culture. Since the contact has been made the UFP's Prime Directive doesn't apply
Based on episodes like TNG's "First Contact", I get the impression that a planet has to actively develop its own warp drive program (not simply be in contact with others who already have it) before the Federation will be able to contact them.
So even if Barzan becomes aware of other (non-Federation) entities which have warp drive, the Prime Directive will still forbid the Federation from making contact - until and unless Barzan develops ITS OWN form of warp travel.