Here's some research that you could also find online.
This is not an exhaustive list, obviously. Just meant as a jumping off place.
I'll likely keep adding research as I come across it, and as I have time.
If you are looking for research PubMed and Google Scholar are good places to start.
Nose Breathing
Akkoca Ö, Oğuz H, Ünlü CE, Aydın E, Ozdel K, Kavuzlu A. Association Between Nasal Obstruction Symptoms and Anxiety. Ear Nose Throat J. 2020 Aug;99(7):448-452. doi: 10.1177/0145561319900747. Epub 2020 Feb 13. PMID: 32050802.
Chambi-Rocha A, Cabrera-Domínguez ME, Domínguez-Reyes A. Breathing mode influence on craniofacial development and head posture. J Pediatr (Rio J). 2018 Mar-Apr;94(2):123-130. doi: 10.1016/j.jped.2017.05.007. Epub 2017 Aug 14. PMID: 28818510.
Eby GA. Strong humming for one hour daily to terminate chronic rhinosinusitis in four days: a case report and hypothesis for action by stimulation of endogenous nasal nitric oxide production. Med Hypotheses. 2006;66(4):851-4. doi: 10.1016/j.mehy.2005.11.035. Epub 2006 Jan 10. PMID: 16406689.
Mangla PK, Menon MP. Effect of nasal and oral breathing on exercise-induced asthma. Clin Allergy. 1981 Sep;11(5):433-9. doi: 10.1111/j.1365-2222.1981.tb01616.x. PMID: 7318162.
Natasha Mirza, Donald C. Lanza, THE NASAL AIRWAY AND OBSTRUCTED BREATHING DURING SLEEP, Otolaryngologic Clinics of North America, Volume 32, Issue 2, 1999, Pages 243-262, ISSN 0030-6665, https://doi.org/10.1016/S0030-6665(05)70128-6.
Price A, Eccles R. Nasal airflow and brain activity: is there a link? J Laryngol Otol. 2016 Sep;130(9):794-9. doi: 10.1017/S0022215116008537. Epub 2016 Aug 1. PMID: 27477330.
Chambi-Rocha A, Cabrera-Domínguez ME, Domínguez-Reyes A. Breathing mode influence on craniofacial development and head posture. J Pediatr (Rio J). 2018 Mar-Apr;94(2):123-130. doi: 10.1016/j.jped.2017.05.007. Epub 2017 Aug 14. PMID: 28818510.
Eby GA. Strong humming for one hour daily to terminate chronic rhinosinusitis in four days: a case report and hypothesis for action by stimulation of endogenous nasal nitric oxide production. Med Hypotheses. 2006;66(4):851-4. doi: 10.1016/j.mehy.2005.11.035. Epub 2006 Jan 10. PMID: 16406689.
Mangla PK, Menon MP. Effect of nasal and oral breathing on exercise-induced asthma. Clin Allergy. 1981 Sep;11(5):433-9. doi: 10.1111/j.1365-2222.1981.tb01616.x. PMID: 7318162.
Natasha Mirza, Donald C. Lanza, THE NASAL AIRWAY AND OBSTRUCTED BREATHING DURING SLEEP, Otolaryngologic Clinics of North America, Volume 32, Issue 2, 1999, Pages 243-262, ISSN 0030-6665, https://doi.org/10.1016/S0030-6665(05)70128-6.
Price A, Eccles R. Nasal airflow and brain activity: is there a link? J Laryngol Otol. 2016 Sep;130(9):794-9. doi: 10.1017/S0022215116008537. Epub 2016 Aug 1. PMID: 27477330.