fix(ui): one-word games must not highlight phantom cross words; review polish

Board-highlight bug (reported on the contour): formedGeometry walked cross words
unconditionally, so in a single-word (one-word-per-turn) game a staged tile sitting
next to a committed tile lit up a green "cross word" the engine ignores — and which
need not even be a real word (the reported "БО lights up green in a one-word ПОПА
play"). Gate the cross-word walk on the game's multipleWordsPerTurn flag. The score
(8) was already correct — a premium square under the main word.

Also, from review:
- the turn strip reads the staged play's "WORD+WORD = N" while composing a legal move,
  reverting to the turn / result text otherwise;
- the Exchange/Pass dialog shows the bag count ("In the bag: N" / "Bag is empty")
  right-aligned in the title row, via a new optional Modal `titleAside`;
- cosmetics: half the turn strip's bottom padding (the plaques below carry their own
  top pad); a top gap above the landscape rack (it sat flush under the docked history);
  more horizontal padding on tab count badges so a 2-3 digit bag count clears the pill
  ends;
- admin console: the game Summary now shows the single-word / multiple-words rule.

Tests: formed single-word case added; full unit (584) + e2e (chromium + webkit, 113
each) green; backend build + adminconsole templates parse. Docs (FUNCTIONAL +_ru,
UI_DESIGN) updated.

backend/internal/adminconsole/templates/pages/game_detail.gohtml

@@ -8,6 +8,7 @@
 <li><b>Dictionary</b> {{.DictVersion}}</li>
 <li><b>Status</b> {{.Status}}{{if .EndReason}} ({{.EndReason}}){{end}}</li>
 <li><b>AI game</b> {{if .VsAI}}🤖 yes{{else}}no{{end}}</li>
+<li><b>Word rule</b> {{if .MultipleWordsPerTurn}}multiple words per turn{{else}}single word per turn{{end}}</li>
 <li><b>Players</b> {{.Players}}</li>
 <li><b>To move</b> seat {{.ToMove}}</li>
 <li><b>Moves</b> {{.MoveCount}}</li>

backend/internal/adminconsole/views.go

@@ -348,8 +348,12 @@ type GameDetailView struct {
 	UpdatedAt   string
 	FinishedAt  string
 	// VsAI marks an honest-AI game (shown as a 🤖 flag in the summary).
-	VsAI  bool
-	Seats []SeatRow
+	VsAI bool
+	// MultipleWordsPerTurn is the game's cross-word rule: true = standard Scrabble (every cross-word
+	// is validated and scored), false = the single-word rule (only the main word along the play
+	// direction counts). Shown in the summary so an operator can tell the rule at a glance.
+	MultipleWordsPerTurn bool
+	Seats                []SeatRow
 	// HasRobot is true when any seat is a robot, gating the robot-target caption;
 	// RobotTargetPct is the configured global play-to-win rate, in percent.
 	HasRobot       bool

backend/internal/server/handlers_admin_console.go

@@ -566,6 +566,7 @@ func (s *Server) consoleGameDetail(c *gin.Context) {
 		Status: g.Status, Players: g.Players, ToMove: g.ToMove, EndReason: g.EndReason,
 		MoveCount: g.MoveCount, CreatedAt: fmtTime(g.CreatedAt), UpdatedAt: fmtTime(g.UpdatedAt),
 		FinishedAt: fmtTimePtr(g.FinishedAt), VsAI: g.VsAI,
+		MultipleWordsPerTurn: g.MultipleWordsPerTurn,
 	}
 	// Resolve seats and detect robot seats; capture the human opponent's timezone, which
 	// anchors the robot's sleep window for the next-move ETA.