How to auto-arrange nodes of a mindmap in TikZ (to avoid overlapping nodes and connections)

Question

There is a library in TikZ for creating mind (or concept) maps (https://pgf-tikz.github.io/pgf/pgfmanual.pdf#section.60).

However, it doesn't seem that intuitive to use. I want nodes to automatically adjust to their content (which can partly be achieved with https://tex.stackexchange.com/a/285655/194783).

Additionally, I want the mind map to be arranged (at least semi-)automatically.

So that things like in this MWE don't happen:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{mindmap}
\begin{document}
\pagestyle{empty}
{\centering
    \makebox[0pt]{
        \begin{tikzpicture}
            [mindmap,
            grow cyclic,
            every node/.style={concept, text width=},
            concept color=teal!40,
            ]
            \node {node}
                child{
                    node {subnode}
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                }
                child{
                    node {subnode}
                    child { node {subnode} }
                    child { node {subnode} }
                }
                child{
                    node {subnode}
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                }
                child{
                    node {subnode}
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                }
                child{
                    node {subnode}
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                }
                child{
                    node {subnode}
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                }
                child{
                    node {subnode}
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                    child { node {subnode} }
                };
        \end{tikzpicture}
    }
    \par
}
\end{document}

I assume, in CSS, one defines margins to have non-overlapping elements.

Part of the solution might include setting dynamic sibling angles (like in https://tex.stackexchange.com/a/118746/194783) and defining a custom growth function (as described in https://tex.stackexchange.com/a/232914/194783).

Edit: To mitigate the problem, I added some code to automatically set the sibling angle based on the number of children of a node. This still doesn't always avoid overlap, though.

I have seen several posts about writing custom growth functions to achieve a special shape. This also often solves overlaps, but I don't want the shapes that are used there.

• How to put level 2 concept mindmap nodes alongside a rectangle
• Mindmaps, method to get regular circle shape for level 4 or 5
• Grow circular tree with forest

For a related problem, there is the forest package suggested, which doesn't entirely help in my case: Overlapping nodes in a tree using TikZ