I heard yet another version from my Chinese friend: the cat was pushed to the river and never arrived because it drowned :(

Quoting this page: https://www.cheng-tsui.com/blog/chinese-zodiac

"Jade Emperor was separated from the animals by a river, and all animals had to attempt the crossing. Rat and Cat, particularly ambitious and clever creatures, wanted to arrive first. Because of their small size, however, they realized they would need help in crossing the river. They climbed atop Ox, relying on Ox’s strength and sturdiness. Mid-journey, Rat pushed Cat off of Ox and into the river."

Thank you for enlightening us about this topic! I was not aware of how cats are viewed in the Vietnamese culture.