I love mandala patterns and those are beautiful. I have thought of trying to do soap like this - I even have a folder with pictures - but I am quite sure I don't have nearly enough patience. I hope you try it
I would maybe try a pipette or small piping bag with a tiny tip or very small squeeze bottles - something like this maybe https://www.amazon.com/gp/product/B01M7X7PRY/?tag=skimlinks_replacement-20. Ebru could work well. My couple of tries at ebru resulted in a few wayward drops, which doesn't matter if you are swirling, but it seems that this needs precision. I'd consider doing two batches - pour the bases first and let them set up while you make a second batch, split off what you need for the colors and pour the remaining into some kind of mold. Yes, for the dots you will need something that stays very fluid.