There’s no API for this. The way you would have to do this is through polling. You can get results off of the catalog in JSON format (redirects to the search API), so if you poll the most recent item created by Roblox and check if it meets your criteria (uploaded not too long ago from the poll time and is a Limited Unique item), then that’s the item.
The URL itself requests for catalog data in JSON format, seen by /catalog/json
SortType=3 is Recently Updated
ResultsPerPage=1 limits the query to one item, meaning the most recently updated item
CreatorID=1 restricts results to assets created by the Roblox account
If you click the link, you’ll see how you get a result that matches if you go directly to the catalog and input these queries in: created by Roblox and Recently Updated filter. The first item on the page will match the data for what that link returns.