I finally take the time to report an rsync slowness pattern that I've been
seeing for years.
Assuming:
a directory with many (> 20K) files, for example a maildir, on the sending
side, and
a partial copy of that directory on the receiving side, with "enough"
missing missing (say 5K),
I got hit by that bug again, and this time I took the time to try to
create a minimal recipe. It turns out that the culprit was the -y flag,
which I had been using to save some bandwidth, but which doesn't work well
when there are "too many" files in a directory.
A simple reproducer