Are we sinful if a sick cat dies after we refrained from treating it due to high costs, and does the Hadith about the woman who entered Hell because of a cat apply to us?

Mercy is a praiseworthy characteristic that a Muslim should possess towards everything, and it is a cause for Allah's mercy. There is no sin in not treating a cat or removing it from the house if there is hardship or cost involved, as this is not obligatory. Sin occurs when one confines it and withholds food and drink from it until it dies. It is permissible to slaughter an animal to relieve it from suffering if there is no hope for its life, according to some scholars.