[PHP 7] convert nested tree to flat

Bonjour a tous,
Nouveau sur le forum je vais essayer d'être plus claire possible.

je possède donc un arbre.

Code:

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array:3 [▼
  0 => array:9 [▼
    "id" => 1
    "parent_id" => null
    "_lft" => 1
    "_rgt" => 18
    "status" => "active"
    "created_at" => "2019-06-18 11:24:01"
    "updated_at" => "2019-06-20 11:23:14"
    "translate" => array:5 [▼
      "id" => 1
      "culture_id" => 1
      "category_id" => 1
      "label" => "Un principal"
      "slug" => "un-principal"
    ]
    "children" => array:2 [▼
      0 => array:9 [▼
        "id" => 2
        "parent_id" => 1
        "_lft" => 2
        "_rgt" => 13
        "status" => "active"
        "created_at" => "2019-06-18 11:45:40"
        "updated_at" => "2019-06-20 11:10:57"
        "translate" => array:5 [▼
          "id" => 3
          "culture_id" => 1
          "category_id" => 2
          "label" => "azerty"
          "slug" => "azerty"
        ]
        "children" => array:4 [▼
          0 => array:9 [▶]
          1 => array:9 [▶]
          2 => array:9 [▶]
          3 => array:9 [▼
            "id" => 12
            "parent_id" => 2
            "_lft" => 11
            "_rgt" => 12
            "status" => "active"
            "created_at" => "2019-06-19 15:54:05"
            "updated_at" => "2019-06-20 11:52:58"
            "translate" => array:5 [▼
              "id" => 23
              "culture_id" => 1
              "category_id" => 12
              "label" => "sous azerty 3"
              "slug" => "sous-azerty-3"
            ]
            "children" => []
          ]
        ]
      ]
      1 => array:9 [▼
        "id" => 3
        "parent_id" => 1
        "_lft" => 14
        "_rgt" => 17
        "status" => "active"
        "created_at" => "2019-06-18 14:07:35"
        "updated_at" => "2019-06-20 11:09:02"
        "translate" => array:5 [▶]
        "children" => array:1 [▼
          0 => array:9 [▼
            "id" => 4
            "parent_id" => 3
            "_lft" => 15
            "_rgt" => 16
            "status" => "active"
            "created_at" => "2019-06-18 14:08:22"
            "updated_at" => "2019-06-18 14:08:22"
            "translate" => array:5 [▼
              "id" => 7
              "culture_id" => 1
              "category_id" => 4
              "label" => "sous querty"
              "slug" => ""
            ]
            "children" => []
          ]
        ]
      ]
    ]
  ]
  1 => array:9 [▼
    "id" => 5
    "parent_id" => null
    "_lft" => 19
    "_rgt" => 22
    "status" => "active"
    "created_at" => "2019-06-18 14:13:14"
    "updated_at" => "2019-06-18 14:13:14"
    "translate" => array:5 [▼
      "id" => 9
      "culture_id" => 1
      "category_id" => 5
      "label" => "Deux principale"
      "slug" => ""
    ]
    "children" => array:1 [▼
      0 => array:9 [▶]
    ]
  ]
  2 => array:9 [▼
    "id" => 7
    "parent_id" => null
    "_lft" => 23
    "_rgt" => 28
    "status" => "active"
    "created_at" => "2019-06-18 16:51:31"
    "updated_at" => "2019-06-20 11:23:25"
    "translate" => array:5 [▶]
    "children" => array:2 [▼
      0 => array:9 [▶]
      1 => array:9 [▶]
    ]
  ]
]

Je cherche a convertir mon nested tree en flat dans ce genre.

Code:

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array:13 [▼
  0 => array:4 [▼
    "id" => 1
    "label" => "Un principal"
    "status" => "active"
    "created_at" => "2019-06-18T11:24:01+02:00"
  ]
  1 => array:4 [▼
    "id" => 2
    "label" => "Un principal > azerty"
    "status" => "active"
    "created_at" => "2019-06-18T11:45:40+02:00"
  ]
  2 => array:4 [▼
    "id" => 6
    "label" => "Un principal > azerty > sous azerty"
    "status" => "active"
    "created_at" => "2019-06-18T16:48:25+02:00"
  ]
  3 => array:4 [▼
    "id" => 9
    "label" => "Un principal > azerty > sous azerty > Sous azerty 2" <-- deja erreur c'est une sous cat de sous azerty
    "status" => "active"
    "created_at" => "2019-06-18T16:53:21+02:00"
  ]
  4 => array:4 [▼
    "id" => 10
    "label" => "Un principal > azerty > sous azerty > Sous azerty 2 > Sous sous azerty 2"
    "status" => "active"
    "created_at" => "2019-06-19T15:20:07+02:00"
  ]
  5 => array:4 [▼
    "id" => 12
    "label" => "Un principal > azerty > sous azerty > Sous azerty 2 > Sous sous azerty 2 > sous azerty 3" <-- idem  sous azerty 3 est une sous cat de sous azerty
    "status" => "active"
    "created_at" => "2019-06-19T15:54:05+02:00"
  ]
  6 => array:4 [▼
    "id" => 3
    "label" => "Un principal > azerty > querty" <-- erreur
    "status" => "active"
    "created_at" => "2019-06-18T14:07:35+02:00"
  ]
  7 => array:4 [▼
    "id" => 4
    "label" => "Un principal > azerty > querty > sous querty"
    "status" => "active"
    "created_at" => "2019-06-18T14:08:22+02:00"
  ]
  8 => array:4 [▼
    "id" => 5
    "label" => "Deux principale"
    "status" => "active"
    "created_at" => "2019-06-18T14:13:14+02:00"
  ]
  9 => array:4 [▼
    "id" => 13
    "label" => "Deux principale > sous deux 1"
    "status" => "active"
    "created_at" => "2019-06-19T16:00:16+02:00"
  ]
  10 => array:4 [▼
    "id" => 7
    "label" => "Trois principal"
    "status" => "active"
    "created_at" => "2019-06-18T16:51:31+02:00"
  ]
  11 => array:4 [▼
    "id" => 11
    "label" => "Trois principal > sous trois 1"
    "status" => "active"
    "created_at" => "2019-06-19T15:52:17+02:00"
  ]
  12 => array:4 [▼
    "id" => 14
    "label" => "Trois principal > sous trois 1 > Sous trois 2" <-- erreur
    "status" => "active"
    "created_at" => "2019-06-20T11:34:43+02:00"
  ]
]

je suis bloqué en fonction du nombre de profondeur, je n'arrive pas reprendre le label du parent correctement.
J'ai cette fonction avec laquelle je me bat.

Code:

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$tree =[];
        $traverse = function ($categories, $prefix = '') use (&$traverse, &$tree) {
 
            foreach ($categories as $category) {
                $prefix = $category->parent_id===null ? '':$prefix;
                $prefix = ($prefix) ? $prefix.' > '.$category->translate->label: $category->translate->label;
 
                $tree[] = collect([
                    'id' => $category->id ,
                    'label' => $prefix,
                    'status' => $category->status ,
                    'created_at' => $category->created_at->format('c')
                ]);
 
                $traverse($category->children, $prefix);
 
            }
            return collect($tree);
        };
 
        $categories = $traverse($categories);

Merci a tous ce qui pourrons me débloquer.