Is the one who severs ties of kinship prevented from ever entering Paradise, like a polytheist, or will he be punished according to the extent of his disobedience and then enter it?

Maintaining kinship ties is obligatory, and severing them is forbidden. The meaning of the Hadith: "A severer of kinship ties will not enter Paradise" is that one who severs kinship ties will not enter Paradise with the first group of entrants. You must maintain your kinship ties as much as possible, for the Sharia did not specify a particular method or extent for maintaining ties; rather, the reference point is custom. Kinship ties are maintained through visiting, calling, corresponding, and greeting. Ignoring intrusive thoughts, seeking Allah's help, and supplicating will aid in getting rid of them. Be keen on what benefits you and strive to achieve the means that protect you from chest tightness and soul depression.