There’s an entire practice around this stemming from yogic philosophy called nadi shoodana—alternate nostril breathing—the theory essentially says doing this can regulate different male and female energies in the body, which are both responsible for different things, including energy levels (hyper vs relaxed).

I can’t personally attest to any of the deeper claims of the theory, but I have used the alternate nostril breathing as part of meditation practice and I can say that focusing on the breath in this way at the very least helps one enter a meditative state, like many other pranayama techniques.

I’ve never dug into the science attempting to prove the proclaimed effects since experientially it helps me enter meditation, which is what I value it for—I’m not so sure its a good use of time trying to validate the overarching theoretical claims of ancient sources—the practices can still be highly beneficial even if the claims aren’t correct, and I think the main benefit of controlled breathing practices relate to meditation. (that said the body is an interconnected system so its totally plausible that regulating the breath, thus the heartbeat, thus the flow of blood throughout the system could have system wide effects).

If nothing else, hopefully these terms help you in your research.