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Planar tri-valent meshes are not possible on cylindrical surfaces.
On positively curved regions such as the round end of your shape it can work fairly simply by planarizing directly even with a fairly arbitrary starting mesh like this.
On negatively curved regions you can have planar polygons with tri-valent vertices if the polygons become concave. This requires significant changes to the geometry of the faces though, and often the mesh connectivity would also need to be changed.
In developable regions such as the cylindrical region near the base there’s no way the faces can be flat, tangent to the surface and with tri-valent vertices.
Consider for example a place where 3 faces meet
There is no possible way to cut these planes so that they meet edge to edge.
You would need to switch to a 4 valent mesh here to follow the curvature.
What is this for?