feat(chat): unread read-receipts with lobby/game dot and history-open ack

Persist per-message read state as a chat_messages.unread_seats bitmask
(migration 00008): a text message seeds every recipient seat's bit, a nudge
only the awaited seat's. A seat's bit clears when the player opens the move
history or chat (POST /games/:id/chat/read, sent only when something is
unread), and a nudge additionally clears when its recipient answers by moving
(a wired game NudgeClearer, dependency-inverted so game keeps off social).

UI shows a per-viewer unread dot in the lobby (next to the opponent) and the
game score bar — the unread_chat game-view flag seeds it from authoritative
REST views, live chat/nudge events raise it. Opening the move history counts
as reading (even without entering chat): the 💬 fade-blinks twice and the
client acks. Admin Messages gains an unread-only filter, a read/unread column,
and a per-message card with the per-seat read breakdown. Observability:
chat_read_duration histogram + chat_unread_messages gauge + social tracing.

backend/README.md

@@ -41,7 +41,11 @@ is exempt), and the `games.list` response carries an `at_game_limit` flag for th
 `internal/social` owns the friend graph (request/accept),
 per-user blocks, and per-game chat with nudges folded in as a message kind; chat
 messages are length-capped, content-filtered (no links/emails/phone numbers,
-including obfuscated forms) and stored with the sender's IP. `internal/account`
+including obfuscated forms) and stored with the sender's IP. Each message carries an
+`unread_seats` read bitmask (a set bit per recipient seat still to read it); `MarkRead`
+clears a reader's bit when they open the move history or chat, and a wired `NudgeClearer`
+clears a nudge when its recipient moves — both record the publish-to-read latency.
+`internal/account`
 gains profile editing and the email confirm-code flow (a `Mailer` seam: SMTP or a
 development log mailer). The engine now also handles **multi-player drop-out**: in
 a 3–4 player game a resignation or timeout drops that seat and the rest play on