Kleshas are what I meant by "desires" in my last post. I was previously not familiar with Ten Fetters, but through reading Chinese articles, they turn out indeed to be important concepts, so thanks again.
It's possible the "ten desires" are inspired by them, though the context has been changed in an important way. The context of ten fetters is that they are the obstacles one must overcome on the way to nirvana, and they are strongly related to the Buddhist cosmology where there are 3 layers of existence, from low to high: Desire Realm, Form Realm, Formless Realm. The first 5 "lower fetters" only exist in Desire Realm (where most humans are), while the 6th and 7th fetters are translated in Chinese as "lust for Form Realm" and "lust for Formless Realm" - the desire to enter or stay in those higher realms.
The divide of the three Realms is so far not mentioned in Touhou. And compared to real Buddhist concepts which are often unintuitive to the modern mind, "attachment to life" and "longing for death" are much more like something a modern writer will come up with.