update-done: minor clean-ups

update-done: minor clean-ups

This is a follow-up for fb8b0869a7bc30e23be175cf978df23192d59118, and makes a
couple of minor clean-up changes:

- The field name in the timestamp file is changed from "TimestampNSec=" to
  "TIMESTAMP_NSEC=". This is done simply to reflect the fact that we parse the
  file with the env var file parser, and hence the contents should better
  follow the usual capitalization of env vars, i.e. be all uppercase.

- Needless negation of the errno parameter log_error_errno() and friends has
  been removed.

- Instead of manually calculating the nsec remainder of the timestamp, use
  timespec_store().

- We now check whether we were able to write the timestamp file in full with
  fflush_and_check() the way we usually do it.