Auto-mummification is a time-honored tradition across all schools of Buddhism, and is practiced by awakened beings to create a field of merit for layfollowers. It’s considered a “whole body relic” versus the smaller relics that awakened beings leave behind. The Buddha was the first one to leave behind his relics. Mahakasyapa, his disciple, was theoretically the first to self-mummify and is supposed to be in a mountain somewhere awaiting the arrival of the next Buddha, Maitreya, when he’ll come out of his mummified state and offer Sakyamuni’s robes to the new Buddha.

The Sixth Patriarch of Chan, Huineng, was also mummified and his mummy is still in the Chinese temple he was Abbott over in the 7th century.

Tu Dao Hanh, a 11th century Vietnamese monk, famously self-mummified by entering a cave and meditating there until his parinirvana.

The monk photoed in the link you shared isn’t Japanese or Tibetan, but a Theravadin monk in Thailand or Cambodia (I forget which off-hand, just trying to establish this is something all schools of Buddhism do, even if it’s not famous everywhere).

AFAIK, there hasn’t been much controversy over mummification. Auto-cremation is the self-immolation tactic that has been more controversial. However, it should be noted that most self-immolators, whether mummified or cremated, ask permission to do so first from their communities. Those that don’t often don’t succeed and aren’t considered awakened beings. This is why when monks and nuns copycatted Thich Quang Duc’s auto-cremation in the 70s, the last couple of them were not considered to be awakened beings, but Duc—who left behind his heart as a relic and asked permission from the council of monastic leaders—is heralded as a true bodhisattva and awakened being.

Source, mostly about auto-cremation, but talks about the history of Buddhist self-immolation in general including mummification:

Burning for the Buddha: Self-immolation in Chinese Buddhism by James A. Benn (2007)

Also Vietnamese Buddhism in America by Thich Minh Quang (2007), a dissertation for Florida State University going into some history of tantra, Dao Hanh and Quang Duc