Is the lack of a sound heart and the lack of forgiveness, despite exchanging greetings and visits on occasions, considered a severance of kinship ties and a sin? And is the least one can do to maintain kinship ties "to honor your kin, even if only with a greeting"?

The mentioned Hadith is "Blū arḥāmakum" (Wet your wombs/kin), meaning, moisten them with connection.

Forgiving the wrongdoer is encouraged in Islamic law, and it is a cause for great reward and abundant good, especially with relatives. Allah, the Almighty, said: {And let them pardon and overlook. Would you not like that Allah should forgive you?}

If you do good to your relatives who cut ties with you, it is as if you are feeding them hot ashes, and you will always have a supporter from Allah against them. Forgiveness increases a servant in honor and dignity, and it is a way to attain Allah's pardon and forgiveness.

Maintaining kinship ties is one of the causes of blessing in sustenance and lifespan. The Messenger of Allah, peace and blessings be upon him, said: "Whoever desires that his provision be expanded for him or his life span be extended, let him maintain his ties of kinship."