Thank you for this great list!

Currently there is only one reference under "Distinguishing Cause from Effect (Bivariate)".
Below are some references published in recent 3 years (in no particular order).
I try to make a high-variance-low-bias list, keeping an eye on the diversity, without bias to a particular kind of methods.
Hope these help.

https://dl.acm.org/doi/abs/10.1145/3292500.3330854 (KDD19)
http://proceedings.mlr.press/v84/bloebaum18a.html (AISTATS18)
http://proceedings.mlr.press/v119/tagasovska20a.html (ICML20)
https://link.springer.com/chapter/10.1007/978-3-319-98131-4_3
https://proceedings.neurips.cc/paper/2018/hash/73fed7fd472e502d8908794430511f4d-Abstract.html
https://proceedings.neurips.cc/paper/2020/hash/a979ca2444b34449a2c80b012749e9cd-Abstract.html
https://arxiv.org/abs/2007.02809 (AAAI21)
http://proceedings.mlr.press/v108/wu20b.html (AISTATS20)
This last is my own work, and to the best of my knowledge, it still keeps the best result on benchmark dataset.
I will publish the code in the recent future.

Cheers,
Pengzhou (Abel)