No. Only the weapons you choose at 3rd level, one melee, one ranged, and again at 6th and 11th level are your Kensei weapons. Unarmed Strikes are separate from weapons. Unarmed Strikes do count when something says Melee Weapon Attack but do not count for Attack with a Melee Weapon.
Is the monks unarmed attack classed as a kensei weapon, for things like deft strike
No. Only the weapons you choose at 3rd level, one melee, one ranged, and again at 6th and 11th level are your Kensei weapons. Unarmed Strikes are separate from weapons. Unarmed Strikes do count when something says Melee Weapon Attack but do not count for Attack with a Melee Weapon.
Confusing, but that’s how it is.
EZD6 by DM Scotty
https://www.drivethrurpg.com/en/product/397599/EZD6-Core-Rulebook?