It does work on my account. Did you check:

• the board has at least one subitem
• the columnId of the subitem column mitht be different

Alternatively, this would work without hardcoding the columnId

{
  boards(ids: $(boardId)) {
    columns(types: [subtasks]) {
      settings_str
    }
  }
}

For some reason, some of my boards have multiple settings_str values.

Example query:

query test {boards(ids:<BOARD_ID>)
  {
    columns
    {settings_str}
  }
}

Output:

{
  "data": {
    "boards": [
      {
        "columns": [
          {
            "settings_str": "{}"
          },
          {
            "settings_str": "{\\"allowMultipleItems\\":true,\\"itemTypeName\\":\\"column.subtasks.title\\",\\"displayType\\":\\"BOARD_INLINE\\",\\"boardIds\\":[XXXXXXX]}"
          },
          {
            "settings_str": "{}"
          },
          {
            "settings_str": "{\\"done_colors\\":[1],\\"labels\\":{\\"0\\":\\"Working on it\\",\\"1\\":\\"Done\\",\\"2\\":\\"Stuck\\"},\\"labels_positions_v2\\":{\\"0\\":0,\\"1\\":2,\\"2\\":1,\\"5\\":3},\\"labels_colors\\":{\\"0\\":{\\"color\\":\\"#fdab3d\\",\\"border\\":\\"#e99729\\",\\"var_name\\":\\"orange\\"},\\"1\\":{\\"color\\":\\"#00c875\\",\\"border\\":\\"#00b461\\",\\"var_name\\":\\"green-shadow\\"},\\"2\\":{\\"color\\":\\"#df2f4a\\",\\"border\\":\\"#ce3048\\",\\"var_name\\":\\"red-shadow\\"}}}"
          },
          {
            "settings_str": "{}"
          }
        ]
      }
    ]
  },
  "account_id": XXXXX
}

You are requesting the setting_str for each column on your board. The board itself does not have a setting_str. If you want to limit to the subtask column you should filter it in your request

query test {boards(ids:<BOARD_ID>)
  {
    columns (types: [subtasks])
    {settings_str}
  }
}