Convert a string tree to array

I think the iterative approach is more readable so maybe provided solution will help you understand how it is done (though it is lightly inspired by Nina's answer)

So what we do is iterate over all objects in the list. Initially, for each object, we set the current nodeList as the final tree. And we iterate over the length of ids.

First, we create the id form the list of ids by dividing the ids array into incrementally larger chunks with slice (['1'], ['1','2'], ['1', '2', '6') and concatenate to a string with :. So we get 1, 1:2, 1:2:6 ids for the first item.

Next, we find a node in currentNodelist by previously constructed id. If we cannot find the node that means we have not added it yet so we need to create and add it (If we find it then we don't need to do add it).

In the next step, we need to go deeper into the tree so we assign the currently created(or the one that we found) node's children as currentNodelist. With this, we traverse the tree deeper by provided ids.

let objs = [
  { id: '1:2:6', ids: ['1', '2', '6'] },
  { id: '1:4', ids: ['1', '4'] },
  { id: '1', ids: ['1'] },
  { id: '1:2', ids: ['1', '2'] },
];

let tree = [];
for (let i = 0; i < objs.length; i++) {
  let obj = objs[i];

  let currentNodeList = tree;
  for (let j = 0; j < obj.ids.length; j++) {
    let id = obj.ids.slice(0, j + 1).join(':');
    let currentNode = currentNodeList.find((node) => node.id === id);

    if (!currentNode) {
      currentNode = {id, children: []};
      currentNodeList.push(currentNode);
    } 

    currentNodeList = currentNode.children;
  }
}

console.log(tree);

I created a simple gif that shows what is happening in the first 2 iterations. The arrow is pointing to currentListNode.

Figure out your algorithm "on paper" first. Let's start with an empty tree and take the first entry: [1, 2, 6].

1. Node 1: add 1 to the tree - it's now the root and the last visited node.
2. Node 2: add child 2 to node 1.
3. Node 6: add child 6 to node 2.

When processing the next entry, [1, 4], 1 is already in the tree - just add 4 to it.

When processing the last entry, [1, 2], be mindful that 2 is also already in the tree.

P.S. It's "children" not "childs".

Building a tree using recursive algorithms

var jsonTree = [{ id: '1:2:6', ids: ['1', '2', '6'] },{ id: '1:4', ids: ['1', '4'] },{ id: '1', ids: ['1'] },{ id: '1:2', ids: ['1', '2'] },]

var newJsonTree = [];
var currentElement = {id: '1',childs: []}
newJsonTree.push(currentElement)

function buildTree(jsonTree, currentElement){
    for(var i=0;i<jsonTree.length;i++){
        var parent = jsonTree[i];
        for(var j=0;j<jsonTree.length;j++){
            var child = jsonTree[j];
            if(child['visited'] != true && child['id'] != currentElement['id'] && child['id'].indexOf(currentElement['id']) == 0 ){
                if(child['id'].split(":").length == currentElement['id'].split(":").length+1){
                    var newElement = {}
                    newElement['id'] = child['id'];
                    newElement['childs'] = [];
                    currentElement['childs'].push(newElement);
                    child['visited'] = true;
                    buildTree(jsonTree, newElement);
                }
            }
        }
    }
}

buildTree(jsonTree, currentElement);
document.write(JSON.stringify(newJsonTree));

result:

[{"id":"1","childs":[{"id":"1:4","childs":[]},{"id":"1:2","childs":[{"id":"1:2:6","childs":[]}]}]}]