"Find subscription by deal" update_time not updated

When I call the API /v1/subscriptions/find/{dealId} i get a result that looks like that.

{
    "success": true,
    "data": {
        "id": xxx,
        "user_id": xxx,
        "deal_id": xxx,
        "is_active": true,
        "cycle_amount": 0,
        "cycles_count": 0,
        "infinite": false,
        "currency": "EUR",
        "start_date": "2023-03-30",
        "end_date": "2023-06-30",
        "description": null,
        "add_time": "2022-02-17 13:01:56",
     ==>"update_time": "2022-04-06 10:42:34"<==,
        "lifetime_value": 160000,
        "cadence_type": "custom",
        "final_status": null
    }
}

thats good sor far. But when i edit the payment schedule ( for example the amount of one payment) the “update_time” becomes no update.

Can anyone help me? How can i see if the payment schedule was updated before i have to get the whole payment schedule by calling /v1/subscriptions/{id}/payments

EDIT:
I can find the date I want in the payment details api/v1/subscriptions/{ID}/payments.
However, I want to see if any payments have been changed before looking in the details.

Also, all payments get the new update date, whether they have been updated or not. And: the add_time is equal to the update_time

{
    "success": true,
    "data": [
        {
            "id": xxxx,
            "subscription_id": x,
            "deal_id": x,
            "is_active": true,
            "amount": 40000,
            "currency": "EUR",
            "change_amount": 0,
            "due_at": "2023-03-30",
            "revenue_movement_type": "none",
            "payment_type": "installment",
            "description": "März 23",
            "add_time": "2022-08-23 14:24:53",
            "update_time": "2022-08-23 14:24:53"
        },
        {
            "id": xxxx,
            "subscription_id": x,
            "deal_id": x,
            "is_active": true,
            "amount": 40000,
            "currency": "EUR",
            "change_amount": 0,
            "due_at": "2023-04-30",
            "revenue_movement_type": "none",
            "payment_type": "installment",
            "description": "April  23",
            "add_time": "2022-08-23 14:24:53",
            "update_time": "2022-08-23 14:24:53"
        },
        {
            "id": xxxx,
            "subscription_id": x,
            "deal_id": x,
            "is_active": true,
            "amount": 40000,
            "currency": "EUR",
            "change_amount": 0,
            "due_at": "2023-05-31",
            "revenue_movement_type": "none",
            "payment_type": "installment",
            "description": "Mai 23",
            "add_time": "2022-08-23 14:24:53",
            "update_time": "2022-08-23 14:24:53"
        },
        {
            "id": xxxx,
            "subscription_id": x,
            "deal_id": x,
            "is_active": true,
            "amount": 40000,
            "currency": "EUR",
            "change_amount": 0,
            "due_at": "2023-06-30",
            "revenue_movement_type": "none",
            "payment_type": "installment",
            "description": "Juni 23",
            "add_time": "2022-08-23 14:24:53",
            "update_time": "2022-08-23 14:24:53"
        }
    ]
}