feat(lobby): enter the game immediately and wait for the opponent inside it

Quick auto-match no longer waits on a separate screen: Enqueue opens a real game seating the caller with an empty opponent seat (new game status 'open') and the player enters it at once. A second human searching the same variant+rule joins that open game; otherwise a background reaper seats a robot after a 90s + random 0-90s wait, pushing a new in-app opponent_joined event that fills the opponent card and re-enables resign and chat in place.

Matchmaking state is now the open games in the database (the in-memory pool, lobby.poll and lobby.cancel are gone), serialised by a per-bucket advisory lock. While a game is open the starter may move on their turn, but resign, chat and nudge are refused; the lobby and opponent card show "searching for opponent".

Schema edited in the baseline (no prod data): 'open' status, nullable game_players.account_id for the empty seat, and a games.open_deadline_at stamp; jet code regenerated.

backend/README.md

@@ -28,9 +28,10 @@ export, per-account statistics on finish, and a background turn-timeout sweeper
 that auto-resigns overdue turns (honouring each player's daily away window). Like
 the engine it is a service/store layer; the HTTP surface lives in the `gateway`.
 
-The lobby and social fabric. `internal/lobby` holds an in-memory
-matchmaking pool (FIFO per variant and per-turn word rule, pairs two humans into an
-auto-match) and
+The lobby and social fabric. `internal/lobby` runs **auto-match** — `Enqueue` opens a
+real game seating the caller with an **empty opponent seat** (status `open`) or, when
+another player already waits for the same variant and per-turn word rule, seats the
+caller into that open game and starts it — and
 friend-game invitations (invite → accept, starting a 2–4 player game once every
 invitee accepts). `internal/social` owns the friend graph (request/accept),
 per-user blocks, and per-game chat with nudges folded in as a message kind; chat
@@ -52,16 +53,17 @@ robot's moves through the public game API as an ordinary seated player (so only
 win (≈ 40%), targets a small score margin, and times its moves with a move-number-aware
 right-skewed delay (quick openings, long endgames), a night-sleep window anchored to the opponent's timezone, and nudge
 behaviour — all derived deterministically from the game seed, so it keeps no extra
-state. The matchmaker now substitutes a pooled robot (matching the game's language) after a 10-second wait and
-exposes `Poll` so a waiting player can collect the started game — it is the **stream-down
-fallback**: while the client is streaming, the live match-found push (enriched with the recipient's
-initial game state) drives it instead.
+state. A background **reaper** seats a pooled robot (matching the game's language) in any open
+game whose wait window — a fixed **90 s** plus a random **0–90 s** (so **90–180 s**) — has
+elapsed, and the waiting starter is told an opponent took the seat by an in-app
+**opponent_joined** push (carrying their refreshed game state) that fills the opponent card and
+re-enables resign and chat in place.
 
 The backend opens to the edge. The route groups gain their first
 handlers (`internal/server/handlers_*.go`): gateway-only session endpoints under
 `/api/v1/internal` (Telegram/guest/email login → mint, resolve, revoke) and a
 slice of authenticated `/api/v1/user` operations (profile, submit play, game
-state, lobby enqueue/poll, chat). The social/account/history operations under
+state, lobby enqueue, chat). The social/account/history operations under
 `/api/v1/user`: `friends/*` (request/respond/cancel/unfriend,
 list/incoming, the one-time `code` issue/redeem), `blocks/*`, `invitations/*`
 (create/accept/decline/cancel/list), `PUT profile`, `email/{request,confirm}`,
@@ -126,7 +128,7 @@ internal/server/     # gin engine, route groups, X-User-ID middleware, probes
 internal/engine/     # in-process scrabble-solver bridge: registry, bag, Game, replay
 internal/game/       # game domain: lifecycle, journal+cache, hint, word-check, GCG, sweeper
 internal/social/     # friend graph, per-user blocks, per-game chat + nudge, content filter
-internal/lobby/      # in-memory matchmaking pool (+ robot substitution) + friend-game invitations
+internal/lobby/      # auto-match (DB-backed open games + robot substitution) + friend-game invitations
 internal/robot/      # human-like robot opponent: account pool, seed-derived strategy, move driver
 internal/adminconsole/ # server-rendered admin console (Go templates + embedded CSS, view models), served at /_gm
 internal/connector/  # backend gRPC client to the Telegram connector (operator broadcasts)