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']);