feat: honest AI opponent in quick game

New Game's quick game gains an explicit opponent selector — 🤖 AI (default)
or 👤 Random player. AI starts a game seated with a pooled robot that joins
and moves at once: no per-move timeout (a 7-day inactivity loss reusing the
turn-timeout sweeper), chat/nudge disabled, no statistics, the opponent shown
as 🤖 everywhere. The random path (disguised robot) is unchanged.

Driven by one game flag (games.vs_ai), set only on AI-started games so the
disguised path is never revealed; Matchmaker.StartVsAI seats the robot
directly (no open pool); the robot replies event-driven via the game service's
after-commit/after-create hook. Wire: vs_ai on EnqueueRequest + GameView.

backend/internal/postgres/migrations/00001_baseline.sql

@@ -102,6 +102,13 @@ CREATE TABLE games (
     open_deadline_at  timestamptz,
     dropout_tiles     text        NOT NULL DEFAULT 'remove',
     multiple_words_per_turn boolean NOT NULL DEFAULT true,
+    -- vs_ai marks an "honest AI" game: the player knowingly plays a robot that joins
+    -- and moves at once (no disguise). It drives the 🤖 display, the disabled chat/nudge,
+    -- the skipped statistics and the robot's immediate, sleepless, nudge-free behaviour.
+    -- The robot-filled auto-match game (the "random player" path) keeps vs_ai=false, so
+    -- the disguised-robot opponent is never revealed. turn_timeout_secs holds the 7-day
+    -- inactivity clock for these games (the per-move timeout is reused as the abandon rule).
+    vs_ai             boolean     NOT NULL DEFAULT false,
     CONSTRAINT games_variant_chk CHECK (variant IN ('scrabble_en', 'scrabble_ru', 'erudit_ru')),
     CONSTRAINT games_status_chk CHECK (status IN ('active', 'finished', 'open')),
     CONSTRAINT games_players_chk CHECK (players BETWEEN 2 AND 4),