From the Guidelines

The relationship between respiratory exercise, cardiac coherence, and the immune system is supported by moderate-level evidence.

Cardiorespiratory fitness has been shown to reduce all-cause and cardiovascular mortality in the general population, with a 10% to 20% reduction in mortality risk for improvement observed 1.
Exercise has immunomodulatory characteristics that may account for some health-promoting effects, including the establishment of a more anti-inflammatory state on the systemic level 1.
Respiratory muscle strength and endurance can be increased with resistive inspiratory muscle training, and exercises to strengthen abdominal muscles are also recommended 1.
Yoga exercises have been demonstrated to improve coordination of the respiratory muscles and of the diaphragm, and to slow down the respiratory rate 1.

The positive impact of exercise-induced immunomodulation is attributable to the long-term establishment of a more anti-inflammatory state on the systemic level, as most Western diseases arise from a phenotype of chronic silent inflammation 1.
Exercise training can improve exercise tolerance by delaying ventilatory limitation during exercise, without altering lung function or the maximum ventilatory capacity 1.
High-intensity exercise is an efficacious stimulus for increasing cardiorespiratory fitness in chronic disease populations, and such increases in fitness are associated with substantial reductions in cardiovascular mortality 1.

The evidence is mostly based on studies in patients with chronic respiratory disease, such as COPD, and chronic heart failure, and may not be generalizable to other populations.
The optimal intensity and duration of exercise training for improving cardiorespiratory fitness and immune function are not well established, and further research is needed to determine the most effective exercise protocols 1.

From the Research

The relationship between exercise and the immune system is well-established, with exercise affecting immune regulation by changing leucocytes, red blood cells, and cytokines 2.
Regular exercise can reduce the risk of chronic metabolic and cardiorespiratory diseases, partially due to its anti-inflammatory effects, but may also suppress immunity and increase susceptibility to infections 2, 3.
Moderate-intensity exercise has been shown to boost the immune system in patients with cardiorespiratory diseases, with anti-inflammatory effects that are vital for overall well-being and resolving longstanding inflammation 4.

Cardiorespiratory coherence has been linked to improvements in health status, with slow breathing training exercise inducing increased cardiorespiratory coherence and nonlinear behavior of heart rate dynamics 5.
The relationship between cardiac coherence and the immune system is not directly established, but exercise has been shown to have a positive impact on both cardiac health and immune function 6, 4.

The level of evidence for the relationship between respiratory exercise, cardiac coherence, and the immune system is based on a combination of studies examining the effects of exercise on immune function and cardiac health 2, 3, 6, 5, 4.
While the evidence suggests a positive relationship between exercise and immune function, as well as between exercise and cardiac health, further research is needed to fully understand the mechanisms underlying these relationships and to establish the long-term effects of cardiorespiratory rehabilitation programs 4.