I mean, I do like the idea, but syncing such a database file is by far the smallest challenge about this (and could be easily achieved today with e.g. Syncthing or Rsync).

The far harder part is getting RSS readers to support the same file format. There is actually a small project (by basically a singular guy), which tries to accomplish this: https://github.com/39aldo39/DecSync
The desktop RSS reader it supports is GTK, though.

Somewhat of a technologically simpler solution might be to self-host FreshRSS.
Unfortunately, it is of course less simple to actually use, unless you have a home server and some sysadmin skills...