Breathing is an important part of drumming because it helps drummers stay relaxed, keep good time, and perform safely: 
Improves performance: Proper breathing helps you use oxygen to produce your best sound and avoid lactic acid buildup in your muscles. 
Maintains good posture: Your diaphragm is part of your core muscles, which help you maintain balance and alignment while playing. 
Promotes relaxation: Breathing with the beat of a drum can soothe the mind and help you focus. 
Helps you keep time: Breathing can help you keep good time, especially during drum fills. 
Here are some breathing exercises you can try: 
Inhale and exhale short breaths for four beats
Inhale and exhale long breaths
Copy the drumming pattern on your legs while breathing deeply in and out
You can also try guided meditations that combine breathing with drumming, such as:
Breathe With Drums: A meditation that starts with slow, deep breathing, then coordinates your breath with the beat of a drum 
1-Minute Of Coherent Breathing With Drums: A guided meditation by Kara Sherman 
(Tribal Drums) Shamanic Breathwork I 3: A guided meditation that includes three rounds of rhythmic breathing 

At Symmetrical Drumming/Drum Lessons Canberra…techniques such as breathing. Activating Vagas nerve, and relaxation, are employed to ‘see’ time and accurately move from one beat to another without rushing to ‘ meet’ that oncoming beat.

https://symmetricaldrummingaustralia.org