Buddhism

While there are arbitrary aspects, it's not like these things are entirely made up without any kind of thread it pulls on, e.g. the West broadly refers to the culture of Europe and the Mediterranean with roots in ancient Greece and Rome, and going even further back some ancient Egypt and western Asian cultures. And in terms of location, places influenced by that culture are usually included, usually due to colonialism places like North America would count even though they aren't in Europe.

Meanwhile the East (clearly a Euro-centric term) broadly refers to the cultures in Asia, including Western Asia ("the Middle East"). Buddhism and Hinduism are "Eastern" in the sense that they originate in India, which is considered part of "the East".

That said, I agree - asceticism in Indian religion doesn't translate to asceticism in Indian culture more broadly, let alone the East (e.g. across Korea, China, Japan, etc.).

That said, it's clearly Eastern in some sense, even if it's just a subset of Eastern culture rather than total.