Jakarta Capital index is growing up at good pace lately post Soeharto rules, as the Municipal and Central Government investing more on Human Resources Development including giving access toward basic and secondary treatment in Healthcare and promote Universal Education with better access for people to reach any stages of Education. Thus giving impetus toward better quality of live and rising burgeoning middle class (especially youth millenials) among Jakarta population. One tend to forget, Jakarta population is mostly at working ages and quite young (in 2020 Jakarta median age is 29.2) with had good entrepreneur aspirations among them.
Thus compared Jakarta to Singapore who had limited scope as their resources is very narrow and limited (especially lands and human resource as a core elements of a country) and now most of the working ages of Lee Kuan Yew era had reaching their pension ages (with median age around 42.2) , and further limited their option to growing further.
Yes essentially the cold war period was most responsible for the gap India and Indonesia have built up with their LRAS (long run aggregate supply) currently....the theoretical maximum frontier of the economy snapshot.
Singapore is lot closer to it in their case, thus you correct it is not easy for them to grow compared to India and Indonesia who have significant more "easy" room to make up. In their (Singapore) case its almost fully dependent on innovation (or deploying others innovation) w.r.t pushing the LRAS itself (i.e the economic frontier)...this is very capital intensive compared to moving the demand curve along existing aggregate supply (i.e bringing more people and resources up to speed).
It is catch 22, the average being behind to someone means you can grow/progress faster, but its because you are behind still. If you are ahead an operating near some theoretical maximum, you cannot grow much or as easily. But it all depends on how society reflects on all of that. Indonesia is simply an immense country and in a whole different ball game to Singapore in first place.