How to detect when an item has passed by a sensor up to a distance of 10cm?
Here's an inductive sensor with a claimed sensing distance up to 20cm:
https://www.seeedstudio.com/Grove-2-Channel-Inductive-Sensor-LDC1612.html It uses the TI LDC1612 chip.
MORE inductive finds:

https://www.htmsensors.com/inductive-proximity-sensors/metalhead-all-metal-sensing-with-io-link/
https://www.automationdirect.com/adc/overview/catalog/sensors_-z-_encoders/inductive_proximity_sensors
https://www.sick.com/us/en/inductive-proximity-sensors/c/g253054

(totally SICK, dude.)