Conversations page, and know what is unread

/api/v1/conversations answered one page, never unread, its read endpoint
did nothing, and DELETE was missing; each conversation cost a query per
member. Now each conversation keeps its newest post (DmGroup.LastPostId,
set as posts arrive, learnt once by migration _013) and pages by it as
Mastodon does, and each persona's ConversationState holds what it read and
what it took off its list:

- unread when someone else wrote last, after what the persona read;
- read marks it so, and writing in a conversation reads it;
- DELETE takes it off the list until a newer message brings it back.

The list reads its states, newest posts, members and accounts in a few
queries per page.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LsXgEaXee4GCU1hwYgPJXw

docs/ROADMAP.md

@@ -59,6 +59,9 @@ Written 2026-10-01 from the original 2023 code, the decePubClient UI, a federati
   - three bugs the first village found, fixed: likes, reactions, votes and downvotes from followers on followers-only
     posts and from circle members were dropped (G-0001); a Follow refused with Mastodon's first-contact 422 was lost for
     good; a persona addressed without being named could not see the post (silent mentions).
+  - direct conversations as Mastodon keeps them (2026-10-05): paged by their newest message, `unread` when someone
+    else wrote last, `read` that sticks, and `DELETE` taking one off the list until a newer message; the list reads its
+    members and newest posts in a few queries, not several per conversation.
 - [ ] P7 Threads, communities, moderation, the social graph
 - [ ] P8 Signatures, discovery, the long tail
 - [x] P9 Reading at volume (owner decision 2026-10-04, back from "Cut"): lists, server-side filters, scheduled posts,