rich: having far more than enough, whether in money and possessions or, by extension, in some good thing
At its core this is an ordinary word for being well off, the plain opposite of poor. It describes someone whose holdings go well beyond what most people around them have. In the first century that meant a thin upper layer of society, not a comfortable modern household, so when the New Testament calls a person rich it is usually pointing to the powerful few, not the many who lived near the edge of survival.
The word keeps that single basic idea of overflowing abundance even when the Bible turns it in very different directions. Most often it names people with material wealth, and in those settings it tends to carry a sharp, even ominous, edge picked up from the Hebrew prophets: the rich are the ones who hoard, oppress, and trust their own security instead of God. The same writers can also use it of wealthy people who follow God well, like Joseph of Arimathea, so the word itself is not a verdict; the surrounding context supplies the praise or the warning.
The second use stretches the same idea past money altogether. To be rich in mercy, rich in faith, or rich toward God is to overflow with that good thing the way a wealthy person overflows with possessions. This is why the New Testament can say woe to the rich in one place and call God rich in mercy in another: it is deliberately reserving real, lasting wealth for what cannot be hoarded, and exposing mere money as the lesser, riskier kind.