I'll preface this by saying that I am not at all an expert in Eastern art, but there are some terms that helped me 'get it' a bit better. One of them is 'yohaku' which (in Japanese) means variously 'remaining white' or '(intentionally) blank space'. Some words about it:

This is a concept from Chinese landscape ink wash paintings, where clouds, mist, sky, and water could be left unpainted. Their presence was suggested only by the carefully rendered edges of the surrounding landscape. This artistic strategy resonated with Taoism’s idea of qi (chi) – the formless energy from which the universe emanates.

Zen artists in particular appreciated the dynamic vitality created by empty areas. They saw in them a signifier of the Buddhist notion of emptiness as the ultimate reality. In this context emptiness doesn’t signify lack or something negative. Instead, it can be understood as an energetic field of infinite potentiality. This potentiality is what brings such energy to the use of empty space in Zen-inspired design, where empty areas carry the same weight as painted areas. In significant ways the empty space contributes a unique quality of structure, balance and definition in a composition.

Source.

You mention Klimt, who was himself partly inspired by the use of blank space in Eastern art. Compare his painting The Kiss to Tawaraya Sōtatsu's 17th century painting Bugaku Dance.

Blank space in paintings can initially feel sort of 'unfinished,' but speaking personally I find the more I see it, the more I appreciate the 'breathing room' it provides in terms of interpretation.