So I inherited a business unit in Marketing Cloud, and we have one triggered email whose data source I can't locate. Is there a way to confirm all the data sources/APIs that are connecting to a particular marketing cloud instance?
As the other user mentioned, you cannot see this information directly. One other place to check would be the Installed Packages. Go to Setup > Platform Tools > Apps > Installed Packages If there are only a few integrations and/or some good naming conventions used, this could help your search. Here's some information about what exactly you will be looking at: https://developer.salesforce.com/docs/atlas.en-us.noversion.mc-app-development.meta/mc-app-development/api-integration.htm