fix(game): clear nudges on game completion

Nudge badges lingered in the lobby on games that ended by turn-timeout,
resignation or forfeit: those paths commit the finish directly, bypassing
the move path's per-mover NudgeClearer, so the awaited seat's nudge was
never marked read. A finished game's nudges are stale, so clear them all.

Add a wired NudgeExpirer (social.ExpireNudges) called from the shared
commit finish block — covering every completion path — and from the
voidGame recovery path. It clears every seat's nudge bits for the game
and leaves chat messages unread; unlike ClearNudges it records no
publish-to-read latency, since a completion is an expiry, not a read.

An integration test reproduces the timeout case (nudge cleared, chat
kept). Docs: ARCHITECTURE §9.1, FUNCTIONAL (+_ru), backend/README.

backend/README.md

@@ -43,8 +43,10 @@ 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. 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.
+clears a reader's bit when they open the move history or chat, a wired `NudgeClearer`
+clears a nudge when its recipient moves, and a wired `NudgeExpirer` clears **all** of a game's
+nudges when it finishes (any completion path) — the first two record the publish-to-read latency,
+the completion expiry does not (it is not a read); chat messages stay unread on completion.
 A friend request (or block) aimed at a **disguised pooled robot** is recorded per game+seat
 in `robot_friend_requests` / `robot_blocks`, never against the shared robot account; a
 background reaper drops a robot friend request once its game has been finished for **7 days**.