In theory the system can operate without any internet connection, as per the question on the external hard drive. However, that would require someone getting the data from the hard drive every few months and taking it to somewhere with better internet to upload.
Typically we set the images to upload either as they are taken or during the next day and the only minimum requirement would be that it can upload all the images from a given night before the next night starts (otherwise you’ll eventually have a large backlog).
We have the actual numbers somewhere I can try to find, but most modern internet connections can handle this pretty well. A newer satellite internet (e.g. Starlink) would also work, but I’m not sure about some of the older satellite technology services. You probably wouldn’t want it to be a cell phone hotspot for example.