Isn't dying to self a central tenet of Christian teaching?

" Truly, truly, I say to you, unless a grain of wheat falls into the earth and dies, it remains alone; but if it dies, it bears much fruit." John 12:24

"I have been crucified with Christ. It is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me. " Galatians 2:20

" For whoever strives to save his life will lose it, but whoever loses his life for my sake will save it. " Mark 8:35

Lots more.

yes, traditionally there are two ways to approach God: cataphatic and apophatic

apophatic is more similar to negation of self

however, it is not the same

the idea is to remove accidental properties until one perceives the essence itself, like peeling an onion with a diamond in the middle

Dying to self versus death of self maybe?

Yes, in Catholicism there are Jesuit spiritual exercises tailored both for priests and shorter for ordinary people, similar in orthodoxy. I think protestants lack that element and that's why meditation is so catchy in America.

Meditation is big in both Catholicism and Protestantism within the U.S. Meditation is catchy now due to some of the research behind it as well as society always looking for the next panacea.

Modern / Hindu / Buddhist meditation (or what i have read and understood) typically centers around emptying one’s self or chanting a certain phrase to reach enlightenment.

Christian meditation is about filling oneself with the Holy Spirit and denying our own selfish desires.

When God gives his law for humanity in the book of Joshua he commands the people to “meditate on it day and night” because that is the way he intends them to know Him better.

The denial of the self or "selfish desires" is the common thread here.

I heard once that the Eastern and Western religions have swapped definitions for meditation and contemplation, so that Christian contemplative prayer is analogous to Eastern meditation.