Compute the tree height automatically

It’s often desirable to compute the height of a tree diagram automatically, like so:

function computeTreeWidth(paths) {
  const root = d3.tree().nodeSize([1, 1])(d3.stratify().path((d) => d.path)(paths));
  const [x1, x2] = d3.extent(root, (d) => d.x);
  return x2 - x1;
}

Plot.plot({
  axis: null,
  height: computeTreeWidth(paths) * 12,
  marginTop: 4,
  marginBottom: 4,
  marginRight: 120,
  marks: [
    Plot.tree(paths, {path: "path", textStroke: "var(--vp-c-bg)", channels: {href: {value: "link", filter: null}}, treeSort: null})
  ]
})

It would be nice if Plot.tree did this automatically, somehow. The above approach is brittle because computeTreeWidth needs to match the behavior of Plot.tree exactly. (For example, it could be wrong if the tree is sorted prior to layout.) And hard-coding the height is also undesirable because the height should be changed if the data changes.

Start by tracing the Plot.tree implementation and its tree layout and sizing behavior, then compare it with the d3.tree and d3.stratify usage shown in the issue. The work is done when Plot.tree derives an appropriate height from the current data and layout, including when sorting or data changes.