Either architect for no data overlap on writes across all the "actives" (in which case software like pgactive could be a good deal) or use a purely distributed database (like Yugabyte).
And I was wondering what other ways, besides schemas, of dividing up 'writer responsibility' would also work? Partitions?
Once you have done that, for updates and deletes you need to keep the same rule (i.e. don't update "foreign" rows).
If you do this, no other technique is needed. Partitions, however, are potentially a good technique to enforce some of these invariants, which gives us quick understanding of where data is originating from given the table name. Same could apply to schemas.
RLS may also help enforce these invariants.