You do not strictly need homing for an open-loop foam cutter — many people just jog to a known start and zero there. But homing makes setups repeatable and is worth adding. Cheap mechanical micro-switches, one per axis, are reliable and easy to configure in FluidNC (direction, feedrate, pull-off).
If you run TMC2209 drivers, you can use StallGuard sensorless homing and skip the switches entirely — the driver detects the motor stalling against the frame as the home reference. It is elegant on a clean build but needs tuning, and on a very lightly loaded foam cutter the stall signal can be touchy, so give yourself time to dial in the threshold and homing speed.
If you run TMC2209 drivers, you can use StallGuard sensorless homing and skip the switches entirely — the driver detects the motor stalling against the frame as the home reference. It is elegant on a clean build but needs tuning, and on a very lightly loaded foam cutter the stall signal can be touchy, so give yourself time to dial in the threshold and homing speed.