In vertical synchronous motor with cylindrical rotor, during no load run under unity power factor condition there is unbalance in motor current observed. what would be the reason?

Puddle of electrons collects at bottom of motor, this is caused by gravity.
Put motor horizontal. Or decrease mass of electrons.

I would think that the unbalance would be caused by unequal phase voltages or unequal motor phase characteristics such as resistance or shorted/damaged windings. How bad is the imbalance? (% motor FLA)

The electrons puddling in the bottom of the motor would pretty much distribute equally causing no imbalance. OTOH a horizontal shaft motor would have the electrons settle to the bottom part of the stator causing a slight imbalance until the motor spun up to speed and the electrons redistributed due to centripetal force. I would think that would happen within a few microseconds of achieving synchronous speeed.