Wifi Thermostat, No C wire on HVAC unit. No control board? Condo
After looking at the schematic for the unit and your picture of the wires with the transformer,  I can help identify what "would" have been a c terminal if it was brought to a connection screw.
In the middle of the schematic,  the wire on the secondary side that is "common" to the relays is referred to as the c wire.
Now in your picture of the transformer is writing on the transformer which identify the secondary side wires.(primary is the high voltage, secondary is the low voltage)
Of those 2, the blue wire connects to the red wire of the schematic (not the c wire), don't touch. The yellow wire connects to the white wire from the schematic ( this is the c wire).
Obviously before you start , be sure to turn off the power to the unit!

And be sure to set the correct system settings in the thermostat. Thermostat electrically behaves differently set for a heat pump vs fan coil vs furnace.
Good luck!