(I am Chinese-born American so I can only speak to my culture.)
Both engagement rings and wedding bands are not from traditional Chinese culture. It's mainly a Western tradition.
Wedding bands became a little more common after the cultural revolution, but still are not as popular as many may think.
Our parents generation may or may not wear wedding bands (my parent's ,who are immigrants, and my in-laws, who are from China, do not). In American or other western countries it is more common, but if you went to Taiwan and China, very few people of our parents generation wear wedding bands and engagement rings are almost non-existent. I always get a lot of compliments when I shop in Taiwan because I am one of the few who wears my wedding band set.
Of course, times are changing, I believe with our generation and future generations, wedding bands are definitely a thing, and engagement rings are becoming more common (and expected

)
(But I noticed that many of my friends or our parents generation, stop wearing their engagement rings after childbirth, probably more for practicality but finger size can and does change after popping out a baby and then it's more of a why be bothered sort of thing.)