Set/unset parent/child fields on issue in next-gen projects via the REST API

[James Sear]

In next-gen projects, epics can have child issues. This is clearly marked as "child" on the epic and as "parent" on the issue. 

As far as I am aware this is a different system from both issue links and epic links (found in classic projects).

I have not found a way to set or unset the parent/child programatically. I have tried:

/rest/api/3/issue/KEY-123

{
  "fields": {
    "parent": {
      "key": "KEY-456"
    }
  }
}

/rest/api/3/issue/KEY-123

{
  "update": {
    "parent": [
      {
        "set": {
          "key": "KEY-456"
        }
      }
    ]
  }
}

One returns a 204 and one returns an error message. Neither work. I've also tried various other combinations using IDs as opposed to keys.

Is this possible?