pKa values around 3 are in general associated to carboxylic groups. Nonetheless pKa values depend also on the neighboring atoms and molecule structure. In the case of pyocyanine the pKa of 4.9 is for a nitrogen atom and it is clearly low from general values associated to amines, which ranged from 9 to 10.
At pH values above 4.9 pyocyanine will be a zwitterion.
Water solubility is largely dictated by symmetry considerations as well as molecule charge. To determine if a phenazine behaves as polar or nonpolar you need to analyze the particular molecule.