Anagram wrote:

Is it common to solder copper pipes under a kitchen sink, or is it almost
universal to use compression connections there?

If you solder under the sink, take great care to not burn anything;
use a heatshield made of steel (not aluminum - melt), preferrably with
some fiberglass or rock wool cloth behind it for thermal insulation.
I've seen scorch marks on almost every job where pipes located near
walls were soldered, and in one case they managed to melt all the low
voltage wires running through metal conduit located 6" from a pipe.