Unable to install auto-bed levelling sensor into my Anet A8
The sensor is working correctly, but the signal is inverted.

Take the obvious solution: invert the endstop from being normally open to normally closed or vice-versa in your firmware.

If you still want to use your existing limit switch in parallel with the sensor (as shown in the video), you will need to switch that one over as well (usually limit switches have 3 contact points, one common, one NC, one NO, so you'd need to move the wire from the NC contact to NO or vice-versa).