To what extent is showing mercy mustahabb?

My apologies in advance for limited knowledge of Islam. I am writing about the topic of mercy, mostly from a Christian perspective, and trying to understand the similarities and differences in the way the two religions use the term 'mercy'. My specific question is whether showing mercy to other people is considered ethically obligatory or optional. I understand the answer may be more complex than just one or the other. Different forms of mercy may fall into different categories. Offering your kidney to save someone's life might not be treated the same ethically as bailing someone out of financial problems or forgiving someone for hurting you. All of those might be considered merciful, but some might be farḍ and others only mustahabb. It might depend on who the person is or on your relationship to them. But in Islamic thinking, what principles are used to decide? If possible, please include some authoritative sources for the answer. Thanks.