Note that GIN does almost what I want, except use the index when sorting by "sent"-timestamp.
So I wonder if RUM can do any better?
What I don't understand is how to have "folder_id" as part of the RUM-index so that I can search in an array of folders using the index, AND have the whole result sorted by "sent"-timestamp also using the RUM-index.
I think you would have to implement an operator for integers for RUM much like btree_gin does for GIN. Sorry don't know how to do that, except to say look in the RUM code to see how it does it for time-stamps.
In the (limited) documentation sorting using timestamp is done like this:
ORDER BY sent <-> '2000-01-01'::TIMESTAMP
which I don't understand; Why must one specify a value here, and how does that value affect the result?
This is essentially identical to ORDER BY ABS(sent - '2000-01-01'::TIMESTAMP); except it can use the index.
So maybe pick a constant outside the range of possible values, and use that as one argument to <->.