You own it as long as they have a license to host and stream it.

They should be offering refunds for this at least, but you literally cannot own something that permanently lives on someone else’s device.

If you want to truly on something, you need to control physical access to it. If there is an option to download the media when you buy it, and you can store it on your own device, then you own it. If not, then you only have access as long as you’re paying someone else for access to their storage.