I can give you an in-depth explanation if you'd like, but the simple version is this: the slime is made up of points on a circle that are connected to every other point with multiple Spring Joint 2D. This is the physics framework for the slime. The slime's visible form is drawn by using each of these points as points on a Bezier spline (for which I used an asset store plugin to create) to get the outline, then generating a mesh to fill in the shape with color.
The movement and momentum stuff is definitely an area for improvement, I agree. Part of the reason the slime loses its momentum when it grows is because of how I did the slime generation that I described above. There's almost certainly a way to improve it.
Thanks again for the playing and feedback. :)