First post here. I had to respond to this closed, old post: forum.arduino.cc/t/360-servo-position-control/579085
There are some newer 360-degree (continuous rotation) servos which have built-in Hall effect encoders. First is this brand new micro-size servo from Feetech: 3.5kg torque micro size digital servo FT2331M 0-360 degree rotation with magnetic encoder - YouTube I don't have one yet, trying to get a sample.
Second is the Feedback 360 from Parallax, which I have used. Works great. Control it using standard servo commands, the feedback is a PWM pulse. I have read it two ways. First, just measuring the pulse width. And second, smoothing the signal with a cap and reading it with an ADC. Both methods worked great. Parallax Feedback 360 Servo - YouTube