How to do this motion graphics?
If I have to make this manually, I would do the following:


Create/Draw the blue Logo in Illustrator as its seen in the final frame.
Breakdown and place spread ink into separate layers, like 4 or more.


To make the drawing animation, create a path "using pen tool" along the lines of the blue Logo, make sure that the path is thick enough to cover the lines.
Using Trim Path effect you can animate the path and as it spread it reveals the blue Logo, kinda like a mask.
The spread of ink is not that obvious, I think it was made using opacity. So whenever you reveal a letter or two, keyframe the opacity of the layer that contains spread ink that you made earlier in Illustrator from 0% to 100% which creates a feel like a spread.
I hope what I wrote does make sense.