feat(stats): best-move word, moves & hint-share, and a hint-count fix (#81)

The statistics screen gains real depth, plus a hint-count bug fix found along the way.

- Best move per variant: the screen shows the actual best-move word (drawn as game
  tiles; a wildcard shows its letter but no value), broken down by game variant, empty
  variants omitted. New account_best_move table, written at game finish.
- Moves & hint share: two new lifetime tiles — the player's play count and the share of
  plays that used a hint — from summed account_stats counters (moves, hints_used).
  Honest-AI games are excluded, like the rest of the stats.
- Hint-count fix: the in-game hint badge no longer goes stale across games. The global
  wallet now rides the wire apart from the per-game allowance (wallet_balance on
  StateView/HintResult/StatsView), so the client reads the live wallet rather than a
  per-game snapshot; game_players.hints_used now counts every hint (allowance + wallet),
  its true per-game total.
- Account merge: sums the new moves/hints_used counters and merges the per-variant best
  moves (higher score kept), which it previously dropped.
- Admin: the user card shows Moves and Hints used.
- UI polish: tab/label wording, game-over text, and e2e selectors hardened against label
  changes.

All wire additions are trailing (backward-compatible). Docs (ARCHITECTURE, FUNCTIONAL +ru,
UISN_DESIGN) updated in step.

gateway/internal/transcode/transcode_social_test.go

@@ -194,7 +194,12 @@ func TestStatsRoundTrip(t *testing.T) {
 		if r.URL.Path != "/api/v1/user/stats" {
 			t.Errorf("unexpected path %q", r.URL.Path)
 		}
-		_, _ = w.Write([]byte(`{"wins":5,"losses":3,"draws":1,"max_game_points":420,"max_word_points":90}`))
+		_, _ = w.Write([]byte(`{"wins":5,"losses":3,"draws":1,"max_game_points":420,"max_word_points":90,` +
+			`"moves":248,"hints_used":12,` +
+			`"best_moves":[{"variant":"scrabble_en","score":90,"word":[` +
+			`{"letter":"c","value":3,"blank":false},` +
+			`{"letter":"a","value":0,"blank":true},` +
+			`{"letter":"t","value":1,"blank":false}]}]}`))
 	})
 	defer cleanup()
 
@@ -208,6 +213,23 @@ func TestStatsRoundTrip(t *testing.T) {
 	if st.Wins() != 5 || st.Losses() != 3 || st.Draws() != 1 || st.MaxGamePoints() != 420 || st.MaxWordPoints() != 90 {
 		t.Fatalf("stats decoded wrong: %+v", st)
 	}
+	if st.Moves() != 248 || st.HintsUsed() != 12 {
+		t.Fatalf("moves/hints decoded wrong: moves=%d hints=%d", st.Moves(), st.HintsUsed())
+	}
+	if st.BestMovesLength() != 1 {
+		t.Fatalf("best moves length = %d, want 1", st.BestMovesLength())
+	}
+	var bm fb.BestMoveView
+	st.BestMoves(&bm, 0)
+	if string(bm.Variant()) != "scrabble_en" || bm.Score() != 90 || bm.WordLength() != 3 {
+		t.Fatalf("best move decoded wrong: variant=%q score=%d wordLen=%d", bm.Variant(), bm.Score(), bm.WordLength())
+	}
+	// The middle tile is a blank: it carries its designated letter but scores 0.
+	var tile fb.BestMoveTile
+	bm.Word(&tile, 1)
+	if string(tile.Letter()) != "a" || tile.Value() != 0 || !tile.Blank() {
+		t.Fatalf("blank tile decoded wrong: letter=%q value=%d blank=%v", tile.Letter(), tile.Value(), tile.Blank())
+	}
 }
 
 func TestGcgRoundTrip(t *testing.T) {