JdbcStreams.java

public <T> T streamQuery(String sql, Function<Stream<SqlRowSet>, ? extends T> streamer, Object... args) {
  return jdbcTemplate.query(sql, resultSet -> {
    final SqlRowSet rowSet = new ResultSetWrappingSqlRowSet(resultSet);
    final boolean parallel = false;

    // The ResultSet API has a slight impedance mismatch with Iterators, so this conditional
    // simply returns an empty iterator if there are no results
    if (!rowSet.next()) {
      return streamer.apply(StreamSupport.stream(Spliterators.emptySpliterator(), parallel));
    }

    Spliterator<SqlRowSet> spliterator = Spliterators.spliteratorUnknownSize(new Iterator<SqlRowSet>() {
      private boolean first = true;
  
      @Override
      public boolean hasNext() {
        return !rowSet.isLast();
      }

      @Override
      public SqlRowSet next() {
        if (!first || !rowSet.next()) {
          throw new NoSuchElementException();
        }
        first = false; // iterators can be unwieldy sometimes
        return rowSet;
      }
    }, Spliterator.IMMUTABLE);
    return streamer.apply(StreamSupport.stream(spliterator, parallel));
  }, args);
}

fun queryStream(sql: String, converter: (SqlRowSet) -> T, args: Array): Stream {
val rowSet = jdbcTemplate.queryForRowSet(sql, *args);
...

Meh, that's totally missing the point!
The idea is lazy consumption (on the fly row processing), but with JdbcTemplate::queryForRowSet you're just aggregating results in memory! For that to workJdbcTemplate would have to keep the db connection open after making that call and it just doesn't do that.
You can replace your whole snippet with jdbcTemplate.queryForList(...).stream() to get the same result.