I know of Nextcloud, but I’m not interested in self-hosting, as I am not an expert in these matters. I’ve been told and read numerous times that you put yourself at more risk by doing things like self-hosting without the expertise to ensure it is actually secure.
That aside, I know there is not currently a way to do what I’m asking for, which is why I’m asking for it. Purism is a company that put out their own laptop hardware, will be releasing their own phone, and has their own distro to go with it all, with their own repo to go with the distro. It is fair to ask if they plan on developing an application to facilitate data transfer along these lines, as it is completely in keeping with the spirit of their stated mission. If they are not currently planning such a feature, it also is fair to ask that they do put effort into it, as it is in keeping with the mission.
Given time and the right developments, Purism has the potential to take Apple on in terms of “quality hardware and software that just works”. They are not there yet, but they have done a wonderful job at making significant progress in this direction. This particular feature I am asking about would be a massive step in that direction for the average person.