If your oxygen level is varying significantly while at rest, you are very out of shape aerobically, and you should be getting more exercise, not obsessing about your breathing patterns.
While it's clear exercise is good for everyone, this statement is not well informed.
For example, oxygen saturation monitoring revealed my at-rest breathing reflex is completely broken due to a known genetic flaw. You know the memes about 'your breathing is now under conscious control'? Mine actually is.
That led to a sleep study-- and, yup, I don't breathe when I'm asleep. I wake every two or three minutes, all night, take a few breaths, and go back to sleep. And have all my life. The mystery of why I'm 'such a light sleeper' also revealed.
Doc I saw about it remarked the mutation is probably more widespread then we know because 'no one is looking for it'. It also completely freaked out a few anesthesiologists.
[There are other reflexes around breathing, and no, I can't just hold me breath as long as I want. The physiological reminders to breathe are pretty strong! But I routinely see my SP02 at rest drop below 70.]
Is this true? I run ~15 miles a week, play pickup basketball 2x a week, and lift weights 3x a week. My oxygen levels can vary 2-5% depending on circadian rhythm at rest. When doing these breathing exercises, I can stabilize it at higher levels. That's at least my experience with it.