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.

The problem is that what you're buying is a license. Of course it has to be a license, because unlike a physical good, anything delivered digitally could be replicated infinitely, and of course you wouldn't be allowed to do something like open your own storefront to resell copies of it. Nor would you legally be allowed to play it on the radio, as background music in a store, etc.

"Buy" isn't really that different here than if you bought a ticket to a concert; of course you wouldn't be able to attend next year with the same ticket, but you still bought something. The problem is that with digital licenses, they can be INCREDIBLY varied, and sellers don't make even a small attempt to clarify what the terms are.

You use the word ownership, but at least from a legal standpoint, that doesn't really mean anything intuitive, unless it means you hold all rights to the IP (which, again, you don't). It would be nice if there was some widespread legal definition and norms about "ownership of a digital copy", but no such concept exists, and frankly the rights holders are not incentivized to try to create something like this.