Based on the execution plan, it looks like the part that takes 13 seconds of the total 14.4 seconds is just calculating the max time used in the where clause. Anytime I see an OR involved in a plan gone off the rails, I always always check if re-writing the query some other way may be faster. How's the plan for something like this?
WHERE message.time = greatest( sub1.time, sub2.time )
/* sub1.time */
(
select MAX ( message2.time ) FROM message AS message2 JOIN thread AS thread2 ON thread2.id = message2.thread JOIN participant ON participant.thread = thread2.id WHERE NOT message2.draft AND participant.identity = 'b16690e4-a3c5-4868-945e-c2458c27a525' AND thread2.spool = spool.id )
/* sub2.time */
( select MAX ( message2.time ) FROM message AS message2 JOIN thread AS thread2 ON thread2.id = message2.thread JOIN participant ON participant.thread = thread2.id JOIN relation ON relation.to = participant.identity AND relation.from = 'b16690e4-a3c5-4868-945e-c2458c27a525' AND relation.manages = TRUE WHERE NOT message2.draft AND thread2.spool = spool.id