Are the two hadiths that address the issue of marriage—one stipulating financial capability, and the other mentioning the Prophet's marrying off a poor man—contradictory, or is the understanding flawed?

The two hadiths do not contradict each other. Ibn Mas'ud's hadith is directed at young people in general, to clarify that marriage is a responsibility and a financial burden, and it guides those who are unable to marry towards fasting as an alternative for chastity. As for Sahl bin Sa'd's hadith, it is a specific case of a poor person who desired marriage, and it contains evidence that poverty alone does not prevent marriage if there is piety and a desire for chastity, and that Allah enriches those who rely on Him, as Allah Almighty says: "If they should be poor, Allah will enrich them from His bounty," and as stated in the hadith: "There are three whom Allah is duty-bound to help: ... and the one who marries, seeking chastity."