Using Big Data to browse Crux, there is data on a country level for each origin. Page Speed Insights includes crux data for origin and also for specific pages.
Is there anyway to get a country breakdown for a single page through the Page Speed Insights API?
There is no way to get a country breakdown through Page Speed Insights, either at an origin or at a page level.
However you can query the Chrome User Experience Report Big Data to get this information.
Please note that the field data shown in Page Speed Insights is a rolling 28 day average, updated daily, whereas the CRUX data is updated once per month so you would get differences.