API - move/restore/unarchive subitem

Hello everyone,
I would appreciate a recommendation for any possible way using JS and/or API to perform the following actions:

  1. Moving a subitem.
  2. Recovering a deleted subitem.
  3. Recovering a subitem that has been archived.

I wish the following GQL command would work to move a subitem to a new parent item. Unfortunately, it gives a column not found error.

mutation {
  change_simple_column_value(
    board_id: 123456, 
    item_id: 654321, 
    column_id: "parent_item", 
    value: "192837"
  ) {
    id
  }
}