Unity FX request / question

Hi guys,
I am a beginner developer and I am trying to recreate this effect for a mobile game in Unity: Painting effect - YouTube .

I tried a few methods. Tried using blend shapes (https://youtu.be/-3r9vCAUtbE), but I don’t think it is a good option.

I think the most promising one would be to have 2 meshes. One for that blob of paint and one for the nail.
They both need to have the same amount of vertices and the point would be to interpolate them when the players clicks.

Here (youtu.be/N-Su8-zpYgk) I just interpolate all the vertices of the 2 meshes at once, but I need them to be controllable by the user as
in the referenced video. The way to go would be to create a raycast from to the mesh and try to move only those vertices and the ones near,
but to achieve the same effect it is a bit more complex and I am not sure how to do it.

I am looking for advices on how to reach that effect or if there is anybody that has done this kind of effect before I am willing to hire them for this.