Must one sacrificial animal be offered, or two, by someone who performed an ‘Umrah as a Mutamatti‘ in Shawwal, then intended to perform another ‘Umrah before the Hajj in the same year?

You are only required to offer one sacrifice (dam) due to your ihram for the second 'Umrah. As for the first 'Umrah, the sacrifice is waived for you because you traveled to Riyadh, as you were not performing tamattu' (a type of Hajj) with it.