feat(ui): single-word rule indicators + auto-match select redesign

Surface the per-game "single word" rule to the client and refine the
random-opponent New Game screen.

- Wire: thread multiple_words_per_turn into the GameView and Invitation
  FlatBuffers tables (Go + TS regenerated), through pkg/wire builders and both
  the backend push-event and gateway REST paths.
- In-game indicators (single-word games only): a small 1 in the status bar's
  score-preview slot (yields to the live preview) and a centred "One word per
  turn" label in the history-drawer header. Standard games show neither.
- Invitation card gains a "One word per turn" line for single-word invitations.
- Auto-match redesign: variant plaques are mutually-exclusive selects (highlight
  on tap, no longer enqueue); a lone offered variant is pre-selected; a bottom
  "Start game" button (disabled until a variant is chosen) confirms. The rule
  toggle appears once a Russian variant is selected.
- Tests: e2e for the new auto flow and the in-game indicator (mock g3 is a
  single-word game); mock/data + fixtures carry the new field. Docs: UI_DESIGN.

pkg/wire/build.go

@@ -30,17 +30,18 @@ type SeatView struct {
 
 // GameView is the shared, non-private game summary.
 type GameView struct {
-	ID               string
-	Variant          string
-	DictVersion      string
-	Status           string
-	Players          int
-	ToMove           int
-	TurnTimeoutSecs  int
-	MoveCount        int
-	EndReason        string
-	Seats            []SeatView
-	LastActivityUnix int64
+	ID                   string
+	Variant              string
+	DictVersion          string
+	Status               string
+	Players              int
+	ToMove               int
+	TurnTimeoutSecs      int
+	MultipleWordsPerTurn bool
+	MoveCount            int
+	EndReason            string
+	Seats                []SeatView
+	LastActivityUnix     int64
 }
 
 // TileRecord is one tile in a decoded MoveRecord (the concrete letter, "?" for a blank
@@ -103,17 +104,18 @@ type InvitationInvitee struct {
 
 // Invitation is a friend-game invitation with its settings and invitees.
 type Invitation struct {
-	ID              string
-	Inviter         AccountRef
-	Invitees        []InvitationInvitee
-	Variant         string
-	TurnTimeoutSecs int
-	HintsAllowed    bool
-	HintsPerPlayer  int
-	DropoutTiles    string
-	Status          string
-	GameID          string
-	ExpiresAtUnix   int64
+	ID                   string
+	Inviter              AccountRef
+	Invitees             []InvitationInvitee
+	Variant              string
+	TurnTimeoutSecs      int
+	HintsAllowed         bool
+	HintsPerPlayer       int
+	MultipleWordsPerTurn bool
+	DropoutTiles         string
+	Status               string
+	GameID               string
+	ExpiresAtUnix        int64
 }
 
 // BuildGameView builds a GameView table from g and returns its offset.
@@ -151,6 +153,7 @@ func BuildGameView(b *flatbuffers.Builder, g GameView) flatbuffers.UOffsetT {
 	fb.GameViewAddPlayers(b, int32(g.Players))
 	fb.GameViewAddToMove(b, int32(g.ToMove))
 	fb.GameViewAddTurnTimeoutSecs(b, int32(g.TurnTimeoutSecs))
+	fb.GameViewAddMultipleWordsPerTurn(b, g.MultipleWordsPerTurn)
 	fb.GameViewAddMoveCount(b, int32(g.MoveCount))
 	fb.GameViewAddEndReason(b, endReason)
 	fb.GameViewAddSeats(b, seats)
@@ -291,6 +294,7 @@ func BuildInvitation(b *flatbuffers.Builder, inv Invitation) flatbuffers.UOffset
 	fb.InvitationAddTurnTimeoutSecs(b, int32(inv.TurnTimeoutSecs))
 	fb.InvitationAddHintsAllowed(b, inv.HintsAllowed)
 	fb.InvitationAddHintsPerPlayer(b, int32(inv.HintsPerPlayer))
+	fb.InvitationAddMultipleWordsPerTurn(b, inv.MultipleWordsPerTurn)
 	fb.InvitationAddDropoutTiles(b, dropout)
 	fb.InvitationAddStatus(b, status)
 	fb.InvitationAddGameId(b, gameID)