I am working on svg animations right now (on Android, but AFAIK it is pretty much the same on the web).
Tooling is pretty poor at the moment, even though this is changing rapidly with :
https://romannurik.github.io/AndroidIconAnimator/
and
that are quickly starting to cover this ground (but they still need a lot of work).
Animating an svg shape to another in a nice way has been doable for some time, like for example : https://material.uplabs.com/posts/animations-in-pocket-casts
Doing so is really time intensive though as soon as your shapes are not trivial, especially since without these two recent tools, you are left with a sheet of paper as your best instrument ..
I would have gladly paid 20 $ last year for a tool allowing me to efficiently create such an animation.