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/notify/encode.go

@@ -42,6 +42,7 @@ func toWireGame(g GameSummary) wire.GameView {
 		EndReason:            g.EndReason,
 		Seats:                seats,
 		LastActivityUnix:     g.LastActivityUnix,
+		NoRepeatWords:        g.NoRepeatWords,
 	}
 }
 

backend/internal/notify/payload.go

@@ -38,6 +38,9 @@ type GameSummary struct {
 	// Kind is the game's origin for the active-game limits (0 unknown, 1 vs_ai, 2 random, 3 friends);
 	// it rides live events so a lobby patch keeps the per-kind count correct.
 	Kind int
+	// NoRepeatWords forbids laying a word that is already on the board (the "Эрудит" rule, pinned
+	// per game); it rides live events so the client's local move preview scores like the server.
+	NoRepeatWords bool
 }
 
 // AlphabetLetter is one variant alphabet entry (a display-only row) embedded in an