That’s an optical slot switch.
Generally any optical switch won’t lose steps, that responsibility falls on the hardware and software design.
to use this on a motor shaft, you also need a slotted disk to interrupt the beam as the motor turns.
If you buy this combined in a single package, it’s called an optical shaft encoder.
OL, to address your questions.
Any (optical) shaft sensor has finite resolution. (pulses per revolution)
How well this works in your application depends on the resolution you need, and the reduction gearing of you motor.
Virtually any motor will work, but again the holding power is also a function of the gear reduction ratio.
Steppers move very precisely if implemented properly, but typically have a limited top speed, and if under load, need to be speed ramped.
Control isn’ta big deal.
DC servomotors (not servos) are somewhat trickier to position accurately, but the gear reduction will make that easier.
Beyond all this, your control circuitry needs to account for gear lash etc, or your motor will hunt around a bit as it reaches the target position.
(snap! Robin2)