“That’s Rich” may not have the protean meanings of some other phrases, like “Shut Up!!” or “Hot Dog!”
See, “Shut Up!” Has 9 Different Meanings? Shut Up!! (No, YOU Shut Up!)”; and “The Many Guises of “Hot Dog.'”
But, it has more definitions than you might initially guess:
One. Caloric. “That chocolate cake sure is rich.”
Two. Hypocritical or ironic ” usually qualified with “a bit.” “Trump crucifying Biden on ethical lapses is a bit rich.” Sarcastically: “Now, THAT’S rich!”
Three. Wealthy. “Sue’s family has money, but nothing like Mary’s. Now, THAT’S rich!” (impressed).
Four. Plentiful; abundant: “The nation’s rich and diverse wildlife.”
Five. Fertile or productive: “rich soil”; “rich mineral deposits.”
Six. A person named “Rich”: “Hey! Isn’t that Rich sitting near the 30-yard line?!?”
Seven. Quintessential behavior for someone named Rich; often preceded with “just so”: “Bob didn’t have a ride to his doctor’s appointment, so Rich drove 20 miles roundtrip at 8 a.m. to take him. That’s just so Rich.”
See also, “Why is Calling Someone a “Piece of Work’ an Insult?” ; “You’re . . . You’re . . . Such an Almond (Huh??)“; “What’s the Past Tense of Sight See?”; “Landmark ” or Watermark?”; “Dried vs. MORE Dried Apricots“; “Wild and Crazy” (vs. Conventional) Fruit; and “What’s the Opposite of “Untold Riches?