The correct numbers are 5743 (2020-08-01) → 5865 (2020-09-21), i.e. 122 or a growth of only about 2%, which is indeed very good. Only Ireland, Italy, China, Belgium are better (and 18 outlier countries adding zero to one deaths only because they each have less than 83 deaths absolute). So, following that definition of "done", I agree Sweden meets it.

But at what cost? Its deaths per capita quotient is horrendous! The thirteen worst countries are:

                  |deaths 2020-09-21|pop in million|deaths/1000 capita
    San Marino                    42         0.0339               1.24
    Peru                       31369        32.5105               0.96
    Belgium                     9950        11.5393               0.86
    Andorra                       53         0.0771               0.69
    Bolivia                     7654        11.5131               0.66
    Spain                      30663        46.7368               0.66
    Chile                      12379        18.952                0.65
    Brazil                    137285       211.0495               0.65
    Ecuador                    11095        17.3737               0.64
    United Kingdom             41877        67.5302               0.62
    US                        199862       329.0649               0.61
    Italy                      35724        60.5501               0.59
    Sweden                      5865        10.0364               0.58

The average for that column is 0.12 and the median is 0.04. It's a really bad trade-off for Sweden to let five to sixteen times more people die than usual just to achieve a small growth rate a couple of months into the pandemic; this does not make any sense. For comparison, Germany's growth in deaths in that time frame was also quite small, namely 2.5%, but they have an under average death quotient of only 0.11.