Do my siblings have a right to the settlement amount from the court judgment regarding the old-tenancy apartment, which I prepared and paid the expenses for its cases, especially after the judgment became solely in my name following my mother's death, and my children will not inherit it after me?

Neither you nor your siblings have any right to this sum. It is obligatory to return it to the apartment owner, as it was not your grandfather's property to be inherited. The old, perpetual lease contract is void, and the tenant must hand over the apartment to its owner upon request without taking any compensation. Any gain or benefit derived from it is unlawful (haram). You must repent to Allah and pay the rent for the period you resided in it, equivalent to the fair market rent (ujrat al-mithl), to the apartment owner. If the owner agrees to waive his right to the fair market rent or to give you some money, there is no objection to accepting it, and your siblings have no right to it.