feat(rules): forbid repeating a word already on the board in Erudit

Russian "Эрудит" treats a word laid on the board as belonging to the
game: it cannot be laid again. Neither the solver, the backend nor the
offline JS port knew the rule, so a player (and the robot) could replay a
word freely. Official Scrabble places no such restriction, so both
Scrabble variants keep playing unrestricted.

The rule applies in two ways. A play whose main word is already on the
board is illegal, and is neither accepted nor generated. A play whose
perpendicular cross-word is already there stands — that word is
incidental to laying the main word — but scores nothing. The set of
played words is the game's own move journal, main words and cross-words
alike, compared decoded, so a word spelled with a blank is the same word.

It lives in the game layer, not the solver: only a game knows its
history, and the solver stays stateless and standard-rules. The backend
applies it at submit, at the move preview and over generated moves
(filtering and re-ranking them, so neither the robot nor the hint can
offer a play the engine would then refuse); the client port does the same
for the offline engine and for the on-device preview of an online game.

The rule is pinned per game (games.no_repeat_words, set from the variant
at creation) rather than keyed on the variant, because a game is replayed
from its journal on every open. Applied retroactively it would make an
already-played repeat illegal — closing that game as a draw — and would
rescore a play whose cross-word repeats an earlier word, shifting a live
game's totals. Games created before the rule keep playing without it. The
flag rides the wire as a trailing field because the client's preview must
score the way the server does, and offline games pin the same answer in
their own record.

backend/internal/game/store.go

@@ -44,6 +44,8 @@ type gameInsert struct {
 	dropoutTiles    string
 	// multipleWordsPerTurn false selects the single-word rule for the game.
 	multipleWordsPerTurn bool
+	// noRepeatWords true forbids laying a word that is already on the board (games.no_repeat_words).
+	noRepeatWords bool
 	// vsAI marks an honest-AI game (games.vs_ai).
 	vsAI bool
 	// kind tags the game's origin (games.game_kind) for the active-game limits.
@@ -173,8 +175,10 @@ func insertGameTx(ctx context.Context, tx *sql.Tx, ins gameInsert, seats []seatI
 		table.Games.Status, table.Games.Players, table.Games.TurnTimeoutSecs,
 		table.Games.HintsAllowed, table.Games.HintsPerPlayer, table.Games.OpenDeadlineAt,
 		table.Games.DropoutTiles, table.Games.MultipleWordsPerTurn, table.Games.VsAi, table.Games.GameKind,
+		table.Games.NoRepeatWords,
 	).VALUES(ins.id, ins.variant, ins.dictVersion, ins.seed, status, ins.players,
-		ins.turnTimeoutSecs, ins.hintsAllowed, ins.hintsPerPlayer, deadline, ins.dropoutTiles, ins.multipleWordsPerTurn, ins.vsAI, int16(ins.kind))
+		ins.turnTimeoutSecs, ins.hintsAllowed, ins.hintsPerPlayer, deadline, ins.dropoutTiles, ins.multipleWordsPerTurn, ins.vsAI, int16(ins.kind),
+		ins.noRepeatWords)
 	if _, err := gi.ExecContext(ctx, tx); err != nil {
 		return fmt.Errorf("insert game: %w", err)
 	}
@@ -1355,6 +1359,7 @@ func projectGame(g model.Games, seats []model.GamePlayers) (Game, error) {
 		UpdatedAt:      g.UpdatedAt,
 	}
 	out.MultipleWordsPerTurn = g.MultipleWordsPerTurn
+	out.NoRepeatWords = g.NoRepeatWords
 	out.VsAI = g.VsAi
 	out.Kind = gamelimits.Kind(g.GameKind)
 	if g.EndReason != nil {