C Wire placement in HVAC?
You are correct

The brown wire from the transformer to the relays in your unit is indeed the C wire you're looking for -- you can cut it and splice it with a bog-standard wirenut, or use a piggyback tab terminal crimped on the end of what you're using for a C wire to make the connection at a device.  There may even be a spare terminal connected to it but nothing else -- the wiring diagram on your unit has provisions for a C wire from the unit to an external compressor contactor.