After some inspection, here's the deal:
fetchall_arrayref always returns an arrayref, which is always a true value. The underlying cursor is finished when the referenced array is empty OR HAS LESS ELEMENTS THAN REQUESTED. Thus, the revised idiom:

while (my $rows = $sth->fetchall_arrayref( [@slice], $maxrows)) {
    last unless @$rows;
    
    # do stuff

    last if @$rows < $maxrows;
}

die $sth->errstr if $sth->errstr;
[download]

which doesn't look that great, with the two lasts and the always-true while $ref (unless some DBD decides to return undef on failure)... can anyone clean it up?