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.

backend/internal/notify/payload.go

@@ -21,17 +21,18 @@ type SeatStanding struct {
 // (mirrors scrabblefb.GameView). LastActivityUnix is the lobby sort key: the current
 // turn's start for an active game, the finish time once finished.
 type GameSummary struct {
-	ID               string
-	Variant          string
-	DictVersion      string
-	Status           string
-	Players          int
-	ToMove           int
-	TurnTimeoutSecs  int
-	MoveCount        int
-	EndReason        string
-	Seats            []SeatStanding
-	LastActivityUnix int64
+	ID                   string
+	Variant              string
+	DictVersion          string
+	Status               string
+	Players              int
+	ToMove               int
+	TurnTimeoutSecs      int
+	MultipleWordsPerTurn bool
+	MoveCount            int
+	EndReason            string
+	Seats                []SeatStanding
+	LastActivityUnix     int64
 }
 
 // AlphabetLetter is one variant alphabet entry (a display-only row) embedded in an
@@ -75,15 +76,16 @@ type InvitationInvitee struct {
 // InvitationSummary is a friend-game invitation carried by the NotifyInvitation event so
 // the client adds it to its lobby list without a refetch (mirrors scrabblefb.Invitation).
 type InvitationSummary 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
 }