Start using the new slog handlers. With this commit we also remove the
need for the LogWriter since we let our LogRotator implement io.Writer
and pass that in to our log file handler.
These are two separate concerns. So this commit splits them up and just
passes a LogWriter from the one to the other. This will become cleaner
in an upcoming commit where the Rotator will implement io.Writer and
there will no longer be a need for LogWriter.
