Are Fingertip Pulse Oximeter Readings Equally Reliable Across Skin Tones?

I’ve seen people question whether fingertip pulse oximeters can overestimate oxygen levels for some patients, particularly people with darker skin. How strong is the evidence for that concern, and does it apply equally to the inexpensive devices people use at home and the monitors used in clinics?

I’m interested in what a single reading can and cannot tell someone, and how researchers compare readings from these devices with more direct measurements. I’m asking for general context, not advice about interpreting a personal medical result.