Convert file paths into JSON structure using bash / jq

Can we convert the below example using jq for bash (https://stedolan.github.io/jq/)?

The requirement is to convert the file paths into json as given in the below example

const data = [
    "/parent/child1/grandchild1"
    "/parent/child1/grandchild2"
    "/parent/child2/grandchild1"
];

const output = {};
let current;

for (const path of data) {
    current = output;

    for (const segment of path.split('/')) {
        if (segment !== '') {
            if (!(segment in current)) {
                current[segment] = {};
            }

            current = current[segment];
        }
    }
}

console.log(output);

The following assumes:

• the input is a valid JSON array of "/"-style pathnames of files;
• pathnames are all absolute (i.e., begin with "/").

reduce .[] as $entry ({};
  ($entry | split("/") ) as $names
   | $names[1:-1] as $p
   | setpath($p; getpath($p) + [$names[-1]]) )

Example

Input

[
    "/parent/child1/grandchild1",
    "/parent/child1/grandchild2",
    "/parent/child2/grandchild3",
    "/parent/child2/grandchild4",
    "/parent2/child2/grandchild5"
]

Output

{
  "parent": {
    "child1": [
      "grandchild1",
      "grandchild2"
    ],
    "child2": [
      "grandchild3",
      "grandchild4"
    ]
  },
  "parent2": {
    "child2": [
      "grandchild5"
    ]
  }
}