Nobody replied. So I had to find out myself, the hard way.
Here is an update for whatever it's worth...
If you ever will consider bringing your kid to Sweden, please be aware that visa will be denied. Why? Well, children born after 2015 are automatically considered to be Swedish citizens, and the embassy can't and won't issue a Schengen visa to a Swede (and it doesn't matter if said person never has had a passport before). I was told to get her a Swedish passport if I wanted to bring her on a vacation to Sweden.
So I still ended up at Department of Consular Affairs at Chaeng Wattana, but not for the documents requested for a visa application. Instead I needed to have the marriage and birth certificates translated and notarized. Translation service was available there; I got approached by a lady who offered this on the spot for a reasonable amount of money. With these things in hand I went, a couple of days later, to the Swedish embassy which will issue a passport once her citizen number has been sorted out (in about two months).