Don’t use deterministic encryption unless your data is already highly random.
Any adversary who knows the distribution of the plaintext data can guess what your encrypted values are, with accuracy that improves as your sample size increases.
There were a bunch of papers on this 10-12 years ago. (Full disclosure: I was an author on some of them.)
Yep, we’ve read the papers. Naveed et al and Grubbs et al primarily.