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.

ui/src/lib/formed.test.ts

@@ -20,14 +20,14 @@ const cells = (g: ReturnType<typeof formedGeometry>) => [...(g?.cells ?? new Set
 
 describe('formedGeometry', () => {
   it('returns null with nothing staged', () => {
-    expect(formedGeometry(board(), [])).toBeNull();
+    expect(formedGeometry(board(), [], true)).toBeNull();
   });
 
   it('finds a fresh horizontal word with no cross words', () => {
     const g = formedGeometry(board(), [
       { row: 7, col: 7 },
       { row: 7, col: 8 },
-    ]);
+    ], true);
     expect(g?.main).toEqual({ row: 7, col: 7, dir: 'H', len: 2 });
     expect(cells(g)).toEqual(['7,7', '7,8']);
   });
@@ -36,14 +36,14 @@ describe('formedGeometry', () => {
     const g = formedGeometry(board(), [
       { row: 7, col: 7 },
       { row: 8, col: 7 },
-    ]);
+    ], true);
     expect(g?.main).toEqual({ row: 7, col: 7, dir: 'V', len: 2 });
     expect(cells(g)).toEqual(['7,7', '8,7']);
   });
 
   it('extends a committed tile into the main word (committed cell in the set)', () => {
     // A committed A at (7,7); a lone tile to its right forms the two-letter main word.
-    const g = formedGeometry(board([[7, 7, 'A']]), [{ row: 7, col: 8 }]);
+    const g = formedGeometry(board([[7, 7, 'A']]), [{ row: 7, col: 8 }], true);
     expect(g?.main).toEqual({ row: 7, col: 7, dir: 'H', len: 2 });
     expect(cells(g)).toEqual(['7,7', '7,8']);
   });
@@ -54,11 +54,23 @@ describe('formedGeometry', () => {
     const g = formedGeometry(board([[6, 8, 'X'], [8, 8, 'Y']]), [
       { row: 7, col: 7 },
       { row: 7, col: 8 },
-    ]);
+    ], true);
     expect(g?.main).toEqual({ row: 7, col: 7, dir: 'H', len: 2 });
     expect(cells(g)).toEqual(['6,8', '7,7', '7,8', '8,8']);
   });
 
+  it('omits cross words under the single-word rule (multipleWords = false)', () => {
+    // The same board as the cross-word case, but a single-word game: the engine ignores the vertical
+    // X-_-Y run (and it need not be a real word), so the geometry must highlight only the main
+    // (horizontal) word — the reported "БО lights up green in a one-word game" bug.
+    const g = formedGeometry(board([[6, 8, 'X'], [8, 8, 'Y']]), [
+      { row: 7, col: 7 },
+      { row: 7, col: 8 },
+    ], false);
+    expect(g?.main).toEqual({ row: 7, col: 7, dir: 'H', len: 2 });
+    expect(cells(g)).toEqual(['7,7', '7,8']);
+  });
+
   it('takes the longer axis as the main word for a lone connecting tile', () => {
     // (7,8) joins a length-3 horizontal (cols 6-8) and a length-4 vertical (rows 5-8): the vertical
     // is longer, so it is the main word and the horizontal becomes a cross word.
@@ -71,6 +83,7 @@ describe('formedGeometry', () => {
         [8, 8, 'E'],
       ]),
       [{ row: 7, col: 8 }],
+      true,
     );
     expect(g?.main).toEqual({ row: 5, col: 8, dir: 'V', len: 4 });
     expect(cells(g)).toEqual(['5,8', '6,8', '7,6', '7,7', '7,8', '8,8']);

ui/src/lib/formed.ts

@@ -77,12 +77,19 @@ function span(
  * formedGeometry derives the composed play's word geometry from the board and the staged tiles.
  * It returns the main word (the maximal run along the play axis through the staged tiles) and the
  * set of every cell the main word and each cross word (a perpendicular run of two or more cells
- * through a staged tile) cover. It returns null when nothing is staged, or when the staged tiles
- * are not on a single line — a shape only an illegal play produces, which the caller never asks
- * about (it is invoked only for a legal preview). The play axis is fixed by the staged tiles when
- * two or more are colinear; a lone tile takes whichever axis forms the longer word.
+ * through a staged tile) cover. Under the **single-word rule** (multipleWords = false) cross words
+ * are omitted, matching the engine, which ignores them entirely — a perpendicular run there is
+ * neither validated nor scored (and need not even be a real word), so highlighting it would be
+ * misleading. It returns null when nothing is staged, or when the staged tiles are not on a single
+ * line — a shape only an illegal play produces, which the caller never asks about (it is invoked
+ * only for a legal preview). The play axis is fixed by the staged tiles when two or more are
+ * colinear; a lone tile takes whichever axis forms the longer word.
  */
-export function formedGeometry(board: Board, pending: readonly Cell[]): FormedGeometry | null {
+export function formedGeometry(
+  board: Board,
+  pending: readonly Cell[],
+  multipleWords: boolean,
+): FormedGeometry | null {
   if (pending.length === 0) return null;
   const filled = filledPredicate(board, pending);
   const first = pending[0];
@@ -115,15 +122,18 @@ export function formedGeometry(board: Board, pending: readonly Cell[]): FormedGe
   }
 
   // Cross words: the perpendicular run through each staged tile, kept only when it is a real word
-  // (two or more cells).
-  const cross: Dir = dir === 'H' ? 'V' : 'H';
-  for (const p of pending) {
-    const cs = span(filled, cross, p.row, p.col);
-    if (cs.len < 2) continue;
-    if (cross === 'H') {
-      for (let c = cs.start; c < cs.start + cs.len; c++) cells.add(key(p.row, c));
-    } else {
-      for (let r = cs.start; r < cs.start + cs.len; r++) cells.add(key(r, p.col));
+  // (two or more cells). Skipped under the single-word rule, where the engine ignores cross words,
+  // so a perpendicular run must not be highlighted as if it were a formed word.
+  if (multipleWords) {
+    const cross: Dir = dir === 'H' ? 'V' : 'H';
+    for (const p of pending) {
+      const cs = span(filled, cross, p.row, p.col);
+      if (cs.len < 2) continue;
+      if (cross === 'H') {
+        for (let c = cs.start; c < cs.start + cs.len; c++) cells.add(key(p.row, c));
+      } else {
+        for (let r = cs.start; r < cs.start + cs.len; r++) cells.add(key(r, p.col));
+      }
     }
   }
 

ui/src/lib/i18n/en.ts

@@ -87,6 +87,7 @@ export const en = {
   'onboarding.gameRack': 'Pick a tile and place it on the board', // rack
 
   'game.bag': '{n} in the bag',
+  'game.bagCount': 'In the bag: {n}',
   'game.bagEmpty': 'Bag is empty',
   'game.hints': 'Hints {n}',
   'game.yourTurn': 'Your turn',

ui/src/lib/i18n/ru.ts

@@ -87,6 +87,7 @@ export const ru: Record<MessageKey, string> = {
   'onboarding.gameRack': 'Выбирайте фишку и ставьте на доску', // rack
 
   'game.bag': '{n} в мешке',
+  'game.bagCount': 'В мешке: {n}',
   'game.bagEmpty': 'Мешок пуст',
   'game.hints': 'Подсказки {n}',
   'game.yourTurn': 'Ваш ход',