Here is one somewhat extreme experiment on rats that showed continual mouth breathing had negative cognitive effects [1]. There is also research that has correlated nasal cycle dominance to different cognitive functions [2]. I’m not totally sure about the covid-19 links this paper makes, but it’s interesting to note the sinuses help create nitric oxide and NO plays a wide range of biological roles [3].
Personally, I do pranayama every morning before seated meditation as well as right before bed and find it to have great emotional benefits if nothing else.
[1] https://www.jstage.jst.go.jp/article/josnusd/61/1/61_18-0006...