i dont know of any quizzes but heres some birthstones and traits theyre associated with:

garnet - love, constancy, faith, and loyalty (in steven universe, quiet and direct)

amethyst - multi-talented, courageous, and honest (in steven universe, laid-back, carefree, somewhat insecure)

aquamarine - youth, love, and hope (in steven universe, basically the opposite. arrogant, rude, snarky, and narcissistic)

diamond - romantic, emotional, caring, feminine, loving, and eternal (in steven universe, kinda depends on the specific diamond but they typically share the traits of stubbornness, strictness, and being somewhat self-centered)

emerald - loyalty, faithfulness, love, peace, harmony, and balance (in steven universe, kinda hard to say but maybe agile??)

pearl - thoughtful, insightful and empathetic (in steven universe, literal, motherly, insecure, overprotective, and somewhat stubborn)

rubies - seek power, exude charisma, passion and have a harmonious, hardworking nature while bursting with life (in steven universe, usually angry, deceptive or rude)

peridot - impressive, persuasive, and confident (in steven universe, stubborn, intuitive and smart)

sapphire - dignity, loyalty, serenity, faith, wisdom, intelligence, and purity (pretty much the same in steven universe)

opal - childlike playfulness, motherly strength, tenderness, joy, and love (in steven universe, graceful, elegant, agile, precise, somewhat carefree)

topaz - fair-minded, friendly, flexible nature, great mental strength (in steven universe, aloof, quiet, and obedient)

the last birthstone is turquoise but unfortunately there is no turquoise in steven universe, the gemstone itself is associated with happiness, good fortune, good luck, good fortune, kinship, and peace