Yep, same database for both Widget and the main app.
It turns out all I had to do was update Core Data's context to the current store generation (in WidgetKit file, getTimeline() function) before making a fetch:
try? Storage.viewContext.setQueryGenerationFrom(.current)
Storage.viewContext.refreshAllObjects()
Found the solution here: https://developer.apple.com/documentation/coredata/accessing_data_when_the_store_has_changed