Ist the documentation for getting CalDAV/CardDAV sync logs faulty?

Yes.

  • | cat > is superfluous anyway, it can be substituted by a simple >. I cannot see any corner-case when this would not apply.
  • tee is always there on SailfishOS, IIRC it is an shell internal command for both bash and busybox (using the usual options Jolla compiles busybox with).
  • It is always nicer to see something while logging, so this is definitely an improvement.