curl --request GET \
  --url https://api.planetscale.com/v1/organizations/{organization}/databases/{database}/branches \
  --header 'Authorization: Bearer <token>'

{
  "current_page": 123,
  "next_page": 123,
  "next_page_url": "<string>",
  "prev_page": 123,
  "prev_page_url": "<string>",
  "data": [
    {
      "id": "<string>",
      "name": "<string>",
      "created_at": "<string>",
      "updated_at": "<string>",
      "deleted_at": "<string>",
      "restore_checklist_completed_at": "<string>",
      "schema_last_updated_at": "<string>",
      "kind": "mysql",
      "mysql_address": "<string>",
      "mysql_edge_address": "<string>",
      "state": "pending",
      "direct_vtgate": true,
      "vtgate_size": "<string>",
      "vtgate_count": 123,
      "cluster_name": "<string>",
      "cluster_iops": 123,
      "ready": true,
      "schema_ready": true,
      "metal": true,
      "production": true,
      "safe_migrations": true,
      "sharded": true,
      "shard_count": 123,
      "stale_schema": true,
      "actor": {
        "id": "<string>",
        "display_name": "<string>",
        "avatar_url": "<string>"
      },
      "restored_from_branch": {
        "id": "<string>",
        "name": "<string>",
        "created_at": "<string>",
        "updated_at": "<string>",
        "deleted_at": "<string>"
      },
      "private_edge_connectivity": true,
      "has_replicas": true,
      "has_read_only_replicas": true,
      "html_url": "<string>",
      "url": "<string>",
      "region": {
        "id": "<string>",
        "provider": "<string>",
        "enabled": true,
        "public_ip_addresses": [
          "<string>"
        ],
        "display_name": "<string>",
        "location": "<string>",
        "slug": "<string>",
        "current_default": true
      },
      "parent_branch": "<string>",
      "vtgate_options": {}
    }
  ]
}