Is it sinful to become a second wife?

No — becoming a second wife through a valid marriage is permissible and not a sin. The Qur'an permits men to marry up to four on strict conditions of fairness — and tells them to marry only one if they fear they cannot be fair — and there were female Companions, including wives of the Prophet ﷺ, who lived in polygynous households. What is sinful is the wrong way of going about it: carrying on a secret relationship, taking another woman's husband by deceit, pressing for the first wife's divorce, or marrying secretly without a wali and registration. Society also should not label a second wife a 'husband-stealer'. See the ruling on polygyny.