So, thebookofshaders.com and godotshaders.com are good places to start to learn this. This is a variation of the ripple effects you can find on godotshaders easily enough.
Basically, it takes a timestamp and x,y of mouse position on hover. Every frame, it draws a circle based on the drops age, using some math to start out fast and then slow down, as if it was spreading like a ripple would.
There's some noise to make it not a perfect circle, a darker rim, and the alpha fades out after a short period. Those give it that watercolor effect layered onto the ripple effects you can find from the links above.
Hope that helps you!