I recently switched from Samsung to iPhone. When watching Netflix on the Samsung device, I could simply go to another app and Netflix would continue as a small video below.
Is this possible with the iPhone 11 or do I not understand something there?
Yes, this is possible, but for the iPhone only from iOS 14, which will appear in the fall.
Either you wait a few more months until iOS 14 is officially available or you install the beta (which is not yet completely stable).
You have been lucky
This will be made possible in the next major update (ios14)
Either wait a few months or install beta (but can cause problems)