If you’re a regular internet user the Personal Data Storage paradigm won’t move your data from the cloud to your personal computer. Most people will still rely on an institutional cloud service, but instead of data-banking with a shareholder-controlled corporation people’s data can be entrusted to the equivalent of member-owned credit unions for data storage.
I can’t say I’d understand what mysterious kind of data it might be that’s stored in social media networks but is owned and used by myself. Really - I don’t have any data I’d want to make use of stored in any social network, except banal stuff like my last few listens at Music Brainz. Usually you’re uploading the sort of data you want to be published to social media. They’re not created there, so why would I need a URL other than
file://with a local path attached to access it. I also seriously doubt that klicking “Save as…” really is some secret and complex ritual known only to immortals and the priest caste, nowadays. (I might be wrong here. I just do not have anything to do with mortals or godfood in my daily life.)