Gula aren is sugar. It is palm sugar, it has a nice caramel taste and a slightly lower glycaemic index than white sugar, and it is 4 calories a gram like every other sugar. A regular kopi susu has 25 to 30g of it in syrup form, about 90 to 110 calories. The 'gula aren is healthier' line is marketing, and the doctor who went viral calculating 370 calories for a homemade version with 4 tablespoons was not exaggerating, that is what four tablespoons does.
The milk is the other half. 150ml of full cream milk is 95 calories with 5g protein, which is the only protein in the cup. Chains that use a mix of fresh milk and creamer or condensed milk push the cup higher, and the ones that use UHT full cream and a heavy hand on the syrup land at 250. The espresso shot itself is 5 calories. You are drinking a milk and sugar drink with coffee flavour.
At Rp 18,000 to 25,000 for a regular, a daily kopi susu is 220 calories a day, 6,600 a month, roughly 0.8kg of fat a month if nothing else changes. That is not a scare number, that is what a daily habit of a 220 calorie drink is. The large size is 350 to 400.
The 'less sugar' option at most chains is real and cuts the syrup by half, to about 170. 'No sugar' takes it to 110, which is basically an iced latte, and at that point it is a reasonable drink with 5g protein.