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/encode_social.go

@@ -91,15 +91,63 @@ func encodeRedeemResult(r backendclient.RedeemResultResp) []byte {
 	return b.FinishedBytes()
 }
 
-// encodeStats builds a StatsView payload.
+// buildBestMoveTile builds a BestMoveTile table and returns its offset.
+func buildBestMoveTile(b *flatbuffers.Builder, t backendclient.BestMoveTileResp) flatbuffers.UOffsetT {
+	letter := b.CreateString(t.Letter)
+	fb.BestMoveTileStart(b)
+	fb.BestMoveTileAddLetter(b, letter)
+	fb.BestMoveTileAddValue(b, int32(t.Value))
+	fb.BestMoveTileAddBlank(b, t.Blank)
+	return fb.BestMoveTileEnd(b)
+}
+
+// buildBestMove builds a BestMoveView table — its word tile vector first, per the
+// bottom-up rule — and returns its offset.
+func buildBestMove(b *flatbuffers.Builder, m backendclient.BestMoveResp) flatbuffers.UOffsetT {
+	tiles := make([]flatbuffers.UOffsetT, len(m.Word))
+	for i, t := range m.Word {
+		tiles[i] = buildBestMoveTile(b, t)
+	}
+	fb.BestMoveViewStartWordVector(b, len(tiles))
+	for i := len(tiles) - 1; i >= 0; i-- {
+		b.PrependUOffsetT(tiles[i])
+	}
+	word := b.EndVector(len(tiles))
+	variant := b.CreateString(m.Variant)
+	fb.BestMoveViewStart(b)
+	fb.BestMoveViewAddVariant(b, variant)
+	fb.BestMoveViewAddScore(b, int32(m.Score))
+	fb.BestMoveViewAddWord(b, word)
+	return fb.BestMoveViewEnd(b)
+}
+
+// encodeStats builds a StatsView payload, embedding the per-variant best moves (each a
+// BestMoveView with its word tiles) when present.
 func encodeStats(r backendclient.StatsResp) []byte {
-	b := flatbuffers.NewBuilder(64)
+	b := flatbuffers.NewBuilder(256)
+	var bestMoves flatbuffers.UOffsetT
+	if len(r.BestMoves) > 0 {
+		offs := make([]flatbuffers.UOffsetT, len(r.BestMoves))
+		for i, m := range r.BestMoves {
+			offs[i] = buildBestMove(b, m)
+		}
+		fb.StatsViewStartBestMovesVector(b, len(offs))
+		for i := len(offs) - 1; i >= 0; i-- {
+			b.PrependUOffsetT(offs[i])
+		}
+		bestMoves = b.EndVector(len(offs))
+	}
 	fb.StatsViewStart(b)
 	fb.StatsViewAddWins(b, int32(r.Wins))
 	fb.StatsViewAddLosses(b, int32(r.Losses))
 	fb.StatsViewAddDraws(b, int32(r.Draws))
 	fb.StatsViewAddMaxGamePoints(b, int32(r.MaxGamePoints))
 	fb.StatsViewAddMaxWordPoints(b, int32(r.MaxWordPoints))
+	fb.StatsViewAddMoves(b, int32(r.Moves))
+	fb.StatsViewAddHintsUsed(b, int32(r.HintsUsed))
+	if len(r.BestMoves) > 0 {
+		fb.StatsViewAddBestMoves(b, bestMoves)
+	}
 	b.Finish(fb.StatsViewEnd(b))
 	return b.FinishedBytes()
 }