Many sites provide a “feed” page, which is a regularly changing XML file* that a program of your choice can read and thus update a list of articles/podcasts etc.

That’s literally all. No accounts or other BS.

That some apps try to make it into a business was to be expected I guess. I have no idea what the (perceived) advantages are, but there’s no need to outsource any of the above into “the cloud”. Plenty of purely local feedreader or podcast apps exist.